Even better, photo-editing software has made it possible to salvage a marginal image. With a few clicks of the mouse, the out-of-frame, out-of-focus, or just "not right" images are jettisoned forever. A few clicks more, and those images with potential are fixed up and made suitable for framing --- a crop here, a red eye changed to brown, the elimination of items cluttering up the background.
But the best pictures aren't made in a software program. They start with the knowledge of how to get great pictures at the first shutter click. Learn these basics and you'll end up with the memories that will last forever:
Taking pictures outside gives your pet a more natural, healthy look. But animals won't sit still like humans. Dogs romp, cats frolic, horses trot. Learn to adjust your aperture and shutter speed to shoot objects in motion, or use predefined program many cameras include. You'll capture the best of your pet's athletic grace.
If your pet is a solid, dark color, use your flash to bring out the detail in his or her face. If you do end up with a red eye, use photo-editing software (basic programs come free with many new cameras and computers) to fix the problem.
If you want a good picture, you need to get on the same plane as your pet. Shoot at eye level or just above the eye level to get the best visual connection. Be careful not to get too low though. A long snout shot from too low an angle can block the eyes, breaking the connection you're trying to get.