A free app for Android, by SmartAppStudio.

SMART Screen Recorder Video Recorder is the best app to capture your smartphone screen easily and quickly. Using this application, you can capture the screen of your smartphone, tablet, or PC, and save the captured images and videos as JPG, PNG, BMP, or GIF files.  

This is a very simple and intuitive tool that allows users to take screenshots and record videos in a simple manner. Users can record the screen of their device with or without the use of root access and record the videos in the form of MP4, MOV, FLV, AVI, or WMV. Users can also edit the captured images and videos and add effects and filters to them.