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Preferably free. I'd like dakka's take on this since normal arcadey phone games are a bit meh.

Benji Bananas is fun.

Not 100% sure if it's on andriod, but gun bro's was a great game on Ipod

Can't find gun bro's in the play store.

says on their site it's for android, I don't think it has the apostrophe,
try just Gun bros

I've heard good things about Plague Inc.

If Fruit Ninja Free is on Android, you should download it, it's pretty fun and doesn't seem any different from the full version at all really.

Hmm are there no decent strategy games around?

I forget the exact game, I think it's called plague or epidemic or pandemic. It's free and loads of fun. You control your own custom disease by giving it symptoms and other stuff, and watch it kill the world.

EDIT: Plague inc is the game, thanks blapblapblap!