These are in no particular order they are just the five games/series I find myself playing the most.
#1. The Zenonia Series is a Great JRPG, always lose track of time playing it.
#2. I have played maplestory since the first year it was out so I play the two Maplestory App Games (They are some of the best RPG games I've played on iOS)
#3. Kairosoft makes great games simulation games.
#4. Pocket God is always fun
#5. and if you like card games Urban Rivals is a MUST PLAY! I've been playing it online for YEARS. Never loses fun.
Others: Resident Evil 4 is great on iOS, Ultimate Mortal Kombat 3 is fun, Assassin's Creed is good, and Cartoon Wars series is Awesome.
Hope you try some! Some of them are free too, like one of the maple story games is, Urban Rivals is, one of the Cartoon Wars is, and a Zenonia is, others might be but I haven't checked in a while.