I really enjoyed Teeny Titans, played it to completion (which I don't do a lot). A couple others that have grabbed me recently:
Guild of Dungeoneering, which is a fun little game where you run a guild and send your little guild members out into dungeons. The little guys can level up a bit but also tend to die a lot, but overall will add to the progression of your guild. It's better than I'm making it sound, and there is not IAP as of yet, you just buy the game and get a whole bunch of content.
World of Warriors, in which you acquire cartoony little warriors that are based on historical people or groups and then you fight with them in turn-based fashion with a very simplistic timing mechanism that can modify your damage done. I'm not super far in but so far it has been a good amount of fun. The one downside is that you run out of 'food' fairly quickly once you get a couple levels in (like after 2-3 fights), so you can only play in brief spurts if you aren't wanting to dump in money.