cogadh: Look at games published by Gameloft. Most of their games are "near AAA" titles, as in they look and play an awful lot like certain games, but aren't those games. I've got a Blur-like racer called Asphalt 6: Adrenaline, a Starcraft-like RTS called Starfront: Collision and a Final Fantasy-like RPG called Eternal Legacy. They also do licensed games and mobile versions of "real" games like Assassin's Creed and Rainbow 6. Just steer clear of their freebie games, most of them are adware ridden and require excessive permissions.
I'd personally steer clear of just about all their games. Shameless rip offs shouldn't be encouraged.
Personally some of the real treats I believe are:
World of Goo
Broken Sword: Shadow of the Templars (the extended one on here)
Great Big War Games, Total War Battles,
A Bards Tale, (xbox port, great game but needs a reasonable spec)
Super Monkeyball 2 Sakura
Beastie Bay
Z Origins (Yup it's ye olde pc game Z)
Blazing Star (one of my all time fave neogeo games, great side scrolling shooter. BONUS!)