I don't usually play games on my phone, but when i do, i play Game Boy games. I still can't belive i lost 19 hours of my life with a Pokemon game.
Gameboy Color A.D. . It's very easy to use and does not need any aditional files to run (like bios, crack, etc.
This screenshot is from Final Fantasy VI for Game Boy Advance. I didn't played it too much , but it can't be bad, i like most of the FF titles. This one needs another emulator, like GameBoid and a bios file. I don't remember where i got this file but it must be easy, like Google search easy.
You can find games for these emulators all over the internet but i preffer http://www.freeroms.com/ .
If you feel like playing something else besides Angry Birds, try these classics, you wont regret.