Closely related to the absolutely essential "must have" apps is the favorite internet bookmarks!
There are MILLIONS of sites that can provide help with learning mandarin, many of which simply aren't useful.
I have found a few true "go to" sites...
1. www.chinesetools.eu - Chinese Character of the Day and the associated Chinese Flashcard are essential daily go to's
2. http://www.columbia.edu/cu/ealac/chinese/resources.html - Columbia University Chinese Language Program
3. http://mind-value.blogspot.com/ - a unique blog of chinese literature, business thinking and biblical understanding