A free program for Android, by Linux Authority.

Screen Recorder is an app to record your phone screen, either apps or games, in high quality. It has a simple interface and works on most Android phones. 

How to use Screen Recorder?

You need to install the app and run it. Just press the appropriate button to start recording the apps, or games. You can record videos with customizable settings: 240p to 1080p, 15FPS to 60FPS, 2Mbps to 30Mbps. To stop the recording process, just shake your phone.

After recording, you can save the HD videos and share them with your friends!