Normally, screen capture is only available if you root your phone because of the security restrictions that Android otherwise imposes.

However, using the Android SDK, there is an alternative method.

1. On your phone go to Settings -> Applications -> Development and then switch on USB Debugging
2. Download the Android-SDK pack to your computer and unzip it
3. Connect your phone to your computer using USB.
4. Open the folder in the SDK pack called tools.
5. Double click ddms.
6. After a brief pause a window should appear named “Dalvik Debug Monitor”.
7. The window is divided into 3 distinct sections – in the top left hand section, under the heading “Name” your phone should be listed. Highlight it.
8. Press CTRL and S to launch the screen capture screen.  Buttons on screen allow you to refresh the image, save, etc. This screen (once you press refresh) should show the current contents of your Android screen.

Thanks to NerdGirl for the info, which I’ve updated (for example, because I found you didn’t have to activate the sync option for it to work).