If you have Android 4.0 or higher:

You can press the Power button + the Volume Down button at the same time to take a screenshot. It will be saved to your gallery.

Note: You need to keep the buttons pressed for around a second for this to work. This is to avoid the screenshot when this combination is accidentally pressed.

UPDATE 8.3.2021: If you have Android 10, you must press the Power button + Volume Down buttons ONLY BRIEFLY (< 0.5 seconds). If you press them longer, the Power menu will just open and the screenshot will not be captured.

If you have an Android lower than 4.0:

If you're rooted: you can install an app called drocap2. This will let you shake your phone, wait on a timer, or click on a notification in your notification bar to take a screenshot and it'll save it to your phone.

If you're not rooted: you can not run a screenshot app on your phone, period. You'll have to install the Android SDK on your computer, connect you phone via USB, and run a program called DDMS. This program is mainly used for developer debugging, but it has a screenshot utility under one of its menus. For a tutorial, see this page. Also, some constructor like Samsung have implemented this function on their phones (the buttons combination change from phone to phone, so search for yours).

In the Galaxy S Froyo (Android 2.2) you can take screenshots by holding the back key and tapping the home button.

Install the Android SDK on your computer, connect the phone and run DDMS from the terminal and then select Device > Screen Capture (or Ctrl+S) and a screenshot will be made.

Once rooted, I've liked working with Screenshot (Cyrket link).

Set the timer, go to your application and wait; or set it to “Shake” mode, go to your application and shake it. Hard. And files show up in a screenshot folder. Happy day.

I mean it. SHAKE IT HARD. Unless there's some trick to shaking and I'm doing it in the wrong direction, this is NOT a sensitive shaker.

UPDATE: yeah, I'm using the timer option. Either the Incredible has a lousy shake sensor, the app is implementing it weirdly, or something else -- but shaking was just ridiculous. Would have been a nice interface, if that worked.

(Variable) Timer to take screenshots works just fine!

Your phone has to be rooted. If it is just search "screenshot" in the market for many options. For an unrooted phone you can use dolphin browser hd with an addon to get screen captures of a website.