As much as we'd like to give a one-word answer, this is one of the trickiest questions in digital photography, so we'll provide a short answer and a long answer.

For any images you plan to print or retouch, we recommend you stick to 3-megapixel resolution and higher; Web- and e-mail-only photos should be fine at resolutions below that. For prints 8x10 or larger, look for digicams with 4-megapixel resolution or higher.

It depends upon what you're doing with the picture and how you're doing it.
Hint: If you're going to display or print pictures at smaller-than-actual-pixel size, resolution doesn't matter much. Opt for the camera with the best colour.

The images below were shot with a 2-megapixel and a 4-megapixel camera, respectively, and scaled down to smaller-than-actual size. Aside from slight colour differences, they should look pretty similar.

2-megapixel	4-megapixel

Hint: If you're going to crop in close or print large, higher resolution lets you crop in closer and get better prints.

Let's say you want to blow up a detail shot or print a picture; that's where extra resolution comes in handy, for both printing and Web display. The 2-megapixel shot (left) is obviously too blurry, but the 3-megapixel (middle) and 4-megapixel (right) shots come pretty close to each other. Which could you live with?

2-megapixel	3-megapixel
4-megapixel