Because a fisheye lens provides such noticeable distortion to your images, it's best for situations where your other wide-angle lenses just aren't enough.
You can create striking portraits with a fisheye lens. Place your subject near the center of the composition and you'll see the way lines in the background bend towards the center of the image. This effect tends to guide a viewer's eyes towards the middle of the frame and draws attention to the person you're shooting.
Pet pictures are especially fun with fisheye lens. If you've ever tried capturing pets in action, you've undoubtedly noticed the way animals almost naturally gravitate towards the lens, ruining the shot with a few good licks on your camera lens. The super wide angle of a fish eye lens lets you shoot very close to your furry friends, and the silly distortion helps accentuate their fun personalities, too.
Because fisheye lenses often have a field of view that's around 180 degrees, you can fit an amazing number of subjects into a single frame. In tight quarters, such as a small room, this large field of view is helpful in capturing groups of people or action shots where fast-moving subjects are hard to capture with a regular lens.
Photo on left by daita. Photo on right by Bill Hails.