Try this application from the market
https://play.google.com/store/apps/details?id=com.ms.screencastfree
** Does not work on Galaxy Nexus or Tegra 2/3 yet **
EDIT 28/11/2014
Lollipop has been released and provides a new Screen recording API
http://developer.android.com/about/versions/android-5.0.html#UI
Screen capturing and sharing
Android 5.0 lets you add screen capturing and screen sharing
capabilities to your app with the new android.media.projection APIs.
This functionality is useful, for example, if you want to enable
screen sharing in a video conferencing app.
The new createVirtualDisplay() method allows your app to capture the
contents of the main screen (the default display) into a Surface
object, which your app can then send across the network. The API only
allows capturing non-secure screen content, and not system audio. To
begin screen capturing, your app must first request the user’s
permission by launching a screen capture dialog using an Intent
obtained through the createScreenCaptureIntent() method.
For an example of how to use the new APIs, see the MediaProjectionDemo
class in the sample project.