I should stop hijacking this thread to talk about 2hu and instead actually post wot i think. Obligatory Fallout 1 and 2
The hallmark of old school RPGs. Barkley, Shut Up and Jam: Gaiden (full title is Tales of Game’s Studios Presents Chef Boyardee’s Barkley, Shut Up and Jam: Gaiden, Chapter 1 of the Hoopz Barkley SaGa)
It's a silly, nonsensical RPG about famous NBA players and a future where basketball is banned. It's free and there's a sequel coming up.
Fistful of Frags
Has the strong competitive aspects of CounterStrike but free and with a higher focus on precision and positioning to achieve high killstreaks. Don't come in expecting cheap spaghetti western action.
Luminous Arc
It's a DS title I usually don't see thrown around when people talk about mobile RPGs. Rather than the usual copypasta job/class turn based combat system you see with Final Fantasy and such, it instead uses a grid map with each of your characters just being a piece on the board with all other enemies and allies. Turn based strategic amazingness along with a fairly interesting story. It has 2 sequels too.
The World Ends With You
Good story, music, and gameplay that will quite literally make you feel pain. Combat works by you multitasking on two screens, one controller by the D Pad and the other by the touch screen. Set in modern day Japan, so it's a break from the typical fantasy settings.