I'm not a big gamer but a few freebies I've been trying and liking, mainly from others' recommendations:
Temple Run - lotsa fun
Major Mayhem - kill, kill, kill
Avenger - kind of confusing, to me,
Hidden Objects, also similar Vacation Quest (but objects are tiny to find)
100 Floors (more on this below) and the related Cheats Guide
Pick a Piggy - took me forever to figure out how to get started
that rat makes me anxious
Where's My Perry/Where's My Water (free versions) - only tried Perry so far but lot's of fun
I tried one auto racing game, Raging Thunder 2, but I think I need something simpler and easier to control.
On 100 Floors: has anyone else tried this game on their Tab? Some of the floors, even using the cheats, seem buggy. Specifically, floors 12, 18 and 26, so far, really aggravated me. Also, sometimes when repeatedly tapping, the Notification window will pop up even when not the tapping is not anywhere near the lower right screen.