I have several favorites but the most important is my security program. There are several good ones - I use lookout mobile security - it has the ability to track my location, make noise even if set to silent, scans all new programs, if someone tries to unlock it too many times incorrectly it takes a picture of them and emails it to me with the time and GPS location. Also backs up a few items - all free. A paid version has more backup features as well as the ability to remotely lock the phone and wipe all info (good if lost or stolen)
A handy android tip: Your android requires a google account which automatically comes with google+ available. Even if you have no intention of using it as a social network it comes with 15GB of storage so I use it to automatically backup my photos and videos. (set to backup on wifi only to avoid data charges) If I loose or destroy my phone, my pictures are safe.
