Dinamalar for Phones This is India's leading Tamil language newspaper. It's a great way to learn the language and also learn about Tamil-speaking regions at the same time.
Tamil Unicode Keyboard free This is the best Tamil keyboard for Android. If you like it you can donate $ or buy the donation version. Proceeds go to Tamil Eelam re-establishment projects.
Tamil Dialog This app is .99 and has some common conversations in Tamil in 6 different categories. Contains the written and audio of the dialogs.
Tamil Lessons 1 This app costs $1.99. It teaches the Tamil alphabet in a myriad of ways to best suit your learning style. Also has testing features. Excellent learning tool!
uTalk Tamil This app costs $9.61 and is a quick and fun way to learn Tamil. It has recording, playback, photos quizzes, and lots more. It's good for learning basic Tamil phrases, not the entire language.