Well, I suppose the main ones I play are:
One Epic Knight - A very fun infinite runner that doesn't try to choke you with IAP's all the time. I have unlocked pretty much everything without ever spending a penny.
Xcom: Enemy Within - Do I really need to say anything here? A fantastic port of a fantastic game that I can play on my PHONE, with hardly any sacrifices made. Only problem with it is that it's a real battery drainer.
Battle for Wesnoth - A port of an open source hex based fantasy strategy. Has an absolute wealth of content, including hundreds of free downloadable add-on's for it. A lot of the sprite work is great and many of the campaigns are fun to play. Definitely should be on your phone if you're a fantasy or strategy fan.
Dead Effect - A pretty fun FPS on the phone. Doesn't cost much, IAP's aren't intrusive (Unlike Dead Trigger 2 which shoves them in your face every few seconds) and controls pretty well for touchscreen. Good if you just wanna shoot stuff.
Deathwatch - A Warhammer strategy game. Pretty good fun, nice to have a decent turn-based Warhammer game on IOS.
Bard's Tale - A Proper RPG on phones. Pretty great, however it is pretty difficult in places, not sure if it's due to the controls or them making it harder but you die real fast by enemy mobs. Still worth getting to have a good chunky RPG on your phone.
Oceanhorn - Basically a Wind Waker rip-off, but it's a very fun one with some great music.
Heroes and Castles 2 - an action/tower defence hybrid. Another fun one to play, though as you get later into the game it starts to feel pretty unbalanced.
Wizorb - A cross between an RPG and breakout, has a great aesthetic and music, and solid gameplay.
Give a search to any of these and you won't be disappointed.
