TwinGo - an arcady sort of puzzler. Hasn't been updated since it's release in 2012 but still has some decent puzzle challenges.
I had gotten Fallout Shelter the day it came out on Android. I'm failing miserably at it. Apart from that, I really like The King of Fighters-A 2012(F). It's a good fighter, and considering it's a free mobile game, it's pretty good.
Got The Cave on my iPod. Pretty cool platform puzzler. I like the variation in stories with the different character scenarios. Controls are maybe a little fussy on the iPod but a decent port.
I'm so glad that this thread still has life! I'm into farm games, had to uninstall one cuzz its picky bout how much memory you need to have to run it otherwise it has connection issues, so if any of you know of a good farm game for android, lemme know follow the buzzards...Don't be afraid, let's go