Okay, time for a blitzkrieg of iOS game suggestions, all of which I currently have installed:
Angry Birds Space (Rovio got stupid with the permissions on the Android version, but the iOS version was recently free and, as far as I can tell, the iOS version doesn't try to sniff out your GPS location to push targeted ads)
Asphalt 8
Azkend
Azkend 2 (prettier than Azkend 1 but not as fun for some reason I can't quite identify)
Bad Air Day (because apparently I'm 12 years old)
Badland
Bookworm Heroes (If you pick it up, add me on Facebook and let's throw down)
Cut the Rope
Fairway Solitaire
Fluffy Diver (The permissions got REALLY stupid on Android, but again, the iOS version seems fine)
Fruit Ninja (for about 5 minutes, anyway)
Funky Smugglers
Got Cow?
Granny Smith
Hungry Sumo
League of Evil 2
Peggle (because it's Peggle, that's why)
Quell+
Puzzle Retreat
Rolling Kongs
Ruzzle (If you play, message me your Ruzzle username and I'll add you. And we'll throw down.)
Shantae: Risky's Revenge (which made me wish I owned a DSi; Risky's Revenge was originally a DSiWare title, which means I can't get it for my DS Lite)
Super Lemonade Factory
Tennis in the Face
Time Surfer
Where's My Water?
All of the games listed above were free at some point or have free/demo versions available on the App Store. Thank you, AppShopper.com!
There are a few other games I enjoyed for a short while, but can't recommend in good conscience because of my disdain for the exploitative and balance-breaking tendencies of free-to-play monetization. Such titles include: Jelly Splash, Plants vs. Zombies 2, Bejeweled Blitz, and Tetris Blitz.