A lot of really good older games have been ported to mobile and work fantastically. Knights of the Old Republic, Neverwinter Nights, and Baldur's Gate just to name a few. Hell, you can play Baldur's Gate multiplayer, cross-platform with PC players even! There's also fo2.exe on the Play Store, which lets you play Fallout 1 & 2 on mobile provided you have access to the files from the PC versions. Oh, and Doom ports galore, of course.
As far as mobile-only or mobile-specific games, my favorite is probably Caves, a surprisingly well done and completely free roguelike.