+1 for Scarface, +1 for Saint's Row, +1 for Crackdown.
I also enjoyed True Crime: New York City. It may have it's issues, but it's not without it's merits too.
I enjoyed playing as a cop, being able to stop & search people, plant evidence, extort shop keepers, chase & arrest random perps.
I also enjoyed the fighting, being able to switch between 3 different martial arts & weapon styles mid fight, dual wielding chickens, performing finishers on stunned opponents.
The car combat was good too, eg being able to overtake someone, perform a 180 switchblade & shoot the driver in the head then do a reverse 180 and carry on your way.
Also being able to store all your weapons in the trunk of your car was a good innovation. Better than the magic pockets of most sandbox games.
It also has a good music soundtrack & a good voice acting cast.