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Don't have others from the Humble Android Bundles?

MD.emu

Scribblenauts remix and Epoch

Knights of pen and paper and any Rayman(fast reactions, but awesome )

Monster Warlord, Spirit Stones...both are great time wasters and do not require your constant attention while playing.

EDGE is a great game :D

Grand theft auto san andreas <3333333333333333

Bike race free

https://play.google.com/store/apps/details?id=com.topfreegames.bikeracefreeworld&hl=es

Superbrothers: Sword & Sworcery EP

Jack Lumber, cool and original game :)

Pixel Dungeon is a great game if you like rogue-likes, and it's free, so that's a plus.
Also Pixel Tower, and Game Dev Story if you're more into tycoon like games.

How about Terraria?, you can spend a whole day in there for all of it's content, at first it can be complicated but it's fun and it has multiplayer like the PC version

Since you said no Angry Birds, how about Bad Piggies? Technically you build stuff in it. :P
(If not, then, sorry, I don't know which other games are for Android.)

Zombies Loli, Sonic Dash, DJ Max Ray, Candy Crush Saga

What about Kairosoft games? There quite a number of them and at least 2 of them are F2P.

Some of the games that I enjoy playing :

• Battleheart
• Cut the rope
• Daddy was a thief
• Falling Fred
• Fruit Ninja
• Plants vs Zombies
• Riptide GP
• SILPHEED Alternative
• Super Hexagon

Some of them might be to your liking.

The four games i play the most atm are Pixel Dungeon(free), Time Surfer($1 i think), Giant Boulder of Death(free), and the Simpson's Tapped out(free)

I got God of Blades from one of the Humble Bundles, it's pretty damn awesome.

Fantasica
Blood Brothers
Defenders of Texel (D.O.T.)

...are the three I was hooked on for a few months.

I recommend "Pocket Mine"

Puzzle and Dragons is an addicting mash up between Puzzle Quest and monster-battling/training RPGs.
Pretty addictive.

Marvel Puzzle Quest. I play it on steam and via android. Mobile is much better.

Badland

Extremely simple controls, great atmosphere, gets challenging as you progress but not so hard that you give up. I love it, and its free.

Run in Crowd, Air Control

Knights of Pen and Paper +1