Don't know how i could pick just 3, but i'm gonna have a go.
Arkham city is probably my all time favourite, not just for the gameplay, the puzzles really got my brain working and when i finally figured them out i was well chuffed. Should hopefully be getting the new game for xmas.
Really loved Shadow of Rome on Ps2, Always loved gladiator stuff and this is my favourite of this type of game, just loved the fact you could cut someones head off then pick it up and throw it at the crowd.
Just wish they would make a new updated version.
Wipeout HD
I'm not a big racing game fan, but add weapons and futuristic vehicles and i'm all for it. Ive unlocked all the levels in the main game (both fury and HD) but mostly I play the eliminator with my daughter. (she's a big fan as well)
Others in the running were
Tenchu (they need to update this too.)
Resident evil 4 (contains my favourite version of mercenaries)
Valkyria chronicles (beautiful strategy based shooter)
Destroy all humans 2 (love all the 60's references)
Hogs of war (used to play it with my daughter when she was little)
Call of duty- black ops ( for Nazi zombie killing madness)
Red dead Revolver (i know the new ones a better game but i love the music in this one)
Uncharted
Kingdom hearts
Hitman absolution
Dead rising 2
Fallout 3- new vegas
Dizzy