Start with a photo. Finish with a masterpiece.
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Orbit the object and try to find a better, more original and more interesting perspective.
Here's an example: It's not hard to take a picture of the Eiffel Tower. You've probably seen tons of images like this:

This image here is somewhat more special:

So is this one:

This one, however, is even more original (though not perfect because of the crooked horizon):

Of course it takes some time and experience to find a more interesting perspective but your efforts will pay off.
Follow the rule of thirds/golden mean.
Divide the image into thirds and place your subject where the lines cross to make it more dynamic. Example:

Source: photoshopnerds.com
Here are some more examples of off-centered objects:


Zoom in more.
By zooming in you can eliminate distracting details and enhance the impact of your photos. In this example image the model is hardly visible because he blends into the background:

By zooming in (i.e. you take the picture again) or cropping the shot (i.e. you use Photoshop) you get an image with more focus on the model, obviously:

If you take a portrait shot, focusing on a specific body part (especially the face and eyes) has a great impact:

Narrow the depth of field.
The depth of field (or DoF) is the portion of a scene that appears sharp in the image. Use a small f-stop number for a narrow DoF and a higher one if you want to increase the sharp area. With a narrow depth of field you can make your main object stand out more by blurring foreground and background objects, as you can see in the image below. However, this means you have to take the shot again, using a low f-stop number. Click here to read more.

Use natural framing.
'Natural framing' means using (usually foreground) elements in the scene to frame your photo. This technique adds depth to your images. In this example the waterscape is framed by the grass and branches:

Tilt your camera.
By tilting your camera a little you can make your shot more dynamic (be careful when taking landscapes or waterscapes, though. A crooked horizon generally does not look good in these cases). Example:

Change the orientation of your image.
Sometimes shifting from landscape to portrait format and vice versa is an easy but effective way to a better photo. Try it ;)
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How to avoid blurry pictures
A tripod is the safest way to sharp pictures, especially when it's combined with a remote control for your camera. If you don't have a remote control, put your camera on a tripod and use the self-timer for optimal results. If you don't have a tripod, a table, chair, pole etc. will do.
If you cannot use a tripod, try to keep the exposure time as short as possible. You can do so by choosing a high ISO setting (but beware: higher ISO means more noise), a larger aperture (i.e. lower f-stop number), and/or a faster shutter speed.
If your camera or lens have an image stabilizing function, make sure it's switched on when not using a tripod. When using a tripod the image stabilizer should be switched off because to minimize movement of parts inside the camera/lens causing blur.

If you use a (D)SLR, hold the grip with your right hand and the lens with your left hand.
When using a compact camera hold it with both hand and try not to hold it too far away from your body to minimize shaking. To stabilize your position, lean yourself against a wall or any other solid object. If you have to kneel, make sure at least one knee is on the ground. You can also press your camera against a solid object.
Take the shot with a photo filter (grad/ND/IR/CPL).
An infrared filter blocks wavelengths less than 720nm. By using this filter the sky becomes dark and anything green, such as trees or grass, becomes white. Click on the image below to learn more about Infrared photography.
View sample images and read more about gradient (grad), neutral density (ND), and polarizing filters on the following websites:
Take a macro shot.
Why not focus on a special part of the object and the beauty of its details? Most compact/bridge cameras have a macro mode (usually indicated by a flower icon), and for (D)SLRs there are macro lenses or macro filters.
This shot of a fly is quite bad because the flower is too distracting and it's hard to see the fly:

This one is a little better because due to the macro lens and its narrow depth of field it focuses entirely on the fly:

But this one is special because it shows something you don't see every day:

If you use a (D)SLR, choose a different lens.
For example, with a fisheye lens and its extreme wideangle perspective you can create a comic effect:

With a tele lens you can zoom in more and focus better on the object:

A macro lens allows you to zoom in even more:

Use a tilt-shift lens to create a "miniature city" effect:

Use a film camera (or another kind of camera such as a lomo camera).
With digital cameras dominating the market, using a film camera may make the picture look more special with intense colors and grain.
Due to their distinct colors, lomo photos are something different compared to the standard digital sauce:

Although Polaroid films are not produced anymore, they were always something special:

If you work at a hospital you could take a couple of really deep portraits with the MRI:

Using X-rays would also make your portrait special ;)

Zoom during exposure to create a warp effect. (DSLR only)
This technique draws the viewer right to the object. Set your camera to shutter speed priority (also called time value priority and abbreviated on your camera with something like 'S' or'Tv') and make sure your shutter speed is slow enough when you zoom. Here are some examples:


This effect can also be simulated with Photoshop. This allows you to take the image with standard settings and leads to a more accurate (i.e. less blurry) result. To do this, open your image with Photoshop and choose Filter > Blur > Radial Blur. Make sure you select the radial method 'Zoom'.
Use a slower/faster shutter speed.
Capturing action in a single frame seems to be a contradiction in terms. However, with the following photography tips you'll be able to freeze movement with ease.

First of all, it is essential for taking action photographs that you have a feeling for your camera and a basic understanding of the sports or action that is going to take place. Take into account that there is always some delay between pressing the shutter and the actual exposure. The better you know your camera and the better you can anticipate the action of your subject, the better your photos will be.
There are basically two techniques you can use to take great action photos: Long exposure and short exposure. This means that for action shots you should set your camera to shutter priority mode, as the shutter speed determines how the action is captured. Additionally, the autofocus should be set to continuous mode. Thus, the camera will
contiuously focus on the moving subject.
Long Exposure (i.e. slow shutter speed)
Choosing a slow shutter speed (long exposure) allows you to add motion blur to the scene. You can either mount your camera on a tripod and capture the action for a relatively long time, which looks great for night shots of heavy traffic, for example. Or you use the panning technique and follow the moving subject along during exposure. This may be difficult at first but practicing this is really worth it. Examples of ideal situations for the panning technique would be a child on a swing, a car driving by, or any other steady motion. In any case, experiment with different shutter speeds. Start with 1/30 seconds and move on to slower speeds gradually.
Short Exposure (i.e. fast shutter speed)
Using a fast shutter speed (short exposure), on the other hand, allows you to freeze the action. This is also called "stop action" photography and looks exceptionally good when small particles are involved that move too fast for the eye to catch. Examples would be a boxer being punched and drops of sweat flying away, a swimmer in "frozen" water, a golfer hitting the ball and parts of soil, or a rally car drifting in sand. In order to really freeze the action, shutter speeds of 1/1000s and faster are recommended, although you can also good results with around 1/250s. For example, the picture on the left was taken with a shutter speed of 1/250s.
Another, more advanced action photography and sports photography tip is the second-curtain flash feature of external flash devices. There the flash fires when the shutter curtain closes, thus freezing the subject while leaving a motion trail behind it.
Take the shot at dusk, dawn, or night to capture it in a more interesting light. Use a flash if necessary.
Compare these two images of the Eiffel Tower. Which one is more interesting?

Pictures taken at dusk or dawn are softer because the light is less intense that at noon:

Cityscapes look best during the 'blue hour' (the hour between sunset and absolute darkness). Grab your tripod and capture this phenomenon with a long exposure. Here you can see why it's actually called 'blue hour':

If you're working in a studio, try changing the lighting setup. Click here to read more.
Why just take one photo when you can do so much more?
Create a tonemapped/HDR image.
A HDR image combines multiple photos of different exposures in one. Thus, highlights appear less bright and shadows less dark--similar to the perception of the human eye. There are a number of programs available for this task, though Photoshop and Photomatix are the most common ones.
Click here to read how to do this with Photoshop.
Click here to read how to do this with Photomatix.

Create a panorama.
Read how to stitch a number of photos together to create a panorama.
In order to create a panorama you have to take a series of shots and stitch them together with a special software. In this tutorial I will show you how to create a panorama.
You'll get the best result when you use a tripod to ensure a perfect horizon (there are even special tripod heads designed for taking panoramas) and set ISO speed and exposure (i.e. aperture and shutter speed) manually to ensure that the images blend perfectly together. If you're not sure which exposure setting is the best, set the camera to auto or program mode, turn toward the brightest area in the landscape and press the shutter half-way through. On the display you will then see the aperture and shutter speed setting your camera would use. Then turn to the darkest area of the landscape and do the same. Take the mean of these two values and set your camera in manual mode accordingly.
Open all the pictures you want to merge with Photoshop. Then click on File > Automate... > Photomerge. The following window will appear:
Click on "Add open images" and press the OK button. Now sit back and relax while Photoshop is aligning the layers and blending the images together automatically. When it's done the panorama will look something like this:

That's it! Now we just have to crop the image. Take the crop tool (C), select the cropping area and click on the checkbox in the top menubar (or simply press enter). For a seamless 360-degree panorama make sure that the left margin begins where the right margin ends, like this:

You're done!
Create a planet using polar coordinates.
To do this, you have to create a panorama first. Then you can "bend" this panorama to a circuar shape. Here's how:

In order to create a panorama you have to take a series of shots and stitch them together with a special software. In this tutorial I will show you how to create a panorama and how to bend it so that it actually looks like a planet.
You'll get the best result when you use a tripod to ensure a perfect horizon (there are even special tripod heads designed for taking panoramas) and set ISO speed and exposure (i.e. aperture and shutter speed) manually to ensure that the images blend perfectly together. If you're not sure which exposure setting is the best, set the camera to auto or program mode, turn toward the brightest area in the landscape and press the shutter half-way through. On the display you will then see the aperture and shutter speed setting your camera would use. Then turn to the darkest area of the landscape and do the same. Take the mean of these two values and set your camera in manual mode accordingly.
Open all the pictures you want to merge with Photoshop. Then click on File > Automate... > Photomerge. The following window will appear:
Click on "Add open images" and press the OK button. Now sit back and relax while Photoshop is aligning the layers and blending the images together automatically. When it's done the panorama will look something like this:

Next we will crop the image. Take the crop tool (C), select the cropping area and click on the checkbox in the top menubar (or simply press enter). For a seamless 360-degree panorama make sure that the left margin begins where the right margin ends, like this:

The next step is the most important one. You have to resize the picture so that the outcome is a square format. To do this, click on Image > Image Size and uncheck the boxes "Scale Styles" and "Constrain Proportions". Then change the height to the amount that is displayed in the "width" field, as demonstrated in the following animation:

After clicking on "OK" your image will look like this:

After that click on Image > Image Rotation > 180°. Your image will change to this:

Next, click on Filter > Distort > Polar Coordinates. Make sure that the checkbox "Rectangular to Polar" is selected and click on OK.

You can fix these flaws by using the spot healing brush tool (J) or the clone stamp tool (S). If the planet does not look spherical, you can also try Filter > Liquify and use the Forward Warp Tool (W) to remove bumps. After retouching your image you can adjust the levels automatically with Image > Adjustments > Levels or by pressing (Ctrl+L) to increase the contrast:

Lastly, rotate and/or flip the image (Image > Image Rotation) and crop it the way you want:

Finally I increased the vibrance and adjusted the levels of the sky (click here to read more about color enhancements), so that my picture eventually looks like this:

Try stereo photography and create a 3D effect using GIF animations.
In this tutorial I will show you how you can create an interesting 3-D effect for your photos by using gif animations. The result will look like this:

This is how it works:

Step 1: Take a photo by looking through the view finder (the LCD screen won’t work well because it’s too inaccurate) with your right eye. Focus on a medium-range object and make sure you include a foreground object as well to get the maximum effect.
Step 2: This is the tricky part because you have to be really accurate. Take a photo by looking through the view finder with your left eye, while focusing on exactly the same point as in step 1 and also keeping exposure, focal lenght, vertical alignment and distance the same. You shouldn’t move the camera lens more than 2,5 inches horizontally (which equals the distance between your eyes) or else the effect will disappear. This may require some experimenting because different cameras have different view finder positions.
Step 3: Open Photoshop and create a new file by pressing Ctrl+N. For the example above I chose a size of 320×240 pixels but you can choose any size you want (however, the width/height ratio should be the same as your camera image ratio, i.e. 4:3, to make the placing process easier). Just keep in mind that animations with no frame delay like the one we are about to create run smoother and without any distortions only when the resolution is relatively low.
Now click on File > Place and select the image that you took in step 1. Place it in the newly created file by pressing the enter key.
Open the animations Window (Window > Animation) and duplicate the first frame by clicking on icon 1 that you can see in the picture below.

Place your other picture from step 2 in the newly created frame (File > Place > Enter).
In the layers window, click on the eye icon of the top layer so that it disappears like in the red circle below:

Now you’re basically done. Test your animation by clicking the play icon (2) in the animations window. If the animation is too shaky, nudge one layer until you get a good result. You might also want to add some sharpness (Filter > Sharpen > Sharpen) or adjust the levels (Layer > New Adjustment Layer > Levels).
If there is no real 3-D effect, try step 1 and 2 again and experiment a bit with the horizontal distance of the two camera positions.
When you’re satisfied with the result, save your animation by clicking File > Save for web, choose GIF format and hit the save button.
Create a photo mosaic.
A photo mosaic consists of many small images that form a large image. Like this (click on the image for full view):
(example image by J2thawiki)
All you need is tons of images (obviously) and mosaic software. A comprehensive tutorial can be found here.
AndreaMosaic: get started right away with a free but powerful mosaic software.
Mac users can download MacOSaiX instead.
Or, check out a Comparison of various mosaic programs at aolej.com.
There are many websites where you can create a mosaic online. However, the results are inferior to the quality you get with a mosaic program, it may take a long time to upload all the images to that site (plus you never know what you sign up to!).
Combine many photos and create a photo manipulation or matte painting.

(example image by Johnrmcconnell)
Check out this list of manipulation techniques to get you started.
Tons of photo manipulations and tutorials can be found at worth1000.com.
If all fails, choose a different object.
This is really the last resort. However, with the techniques described above you should be able to take a mindblowing shot of any object ;)
I took a better photo. What's next?