Surprised nobody's mentioned Red Faction: Guerilla. You have to lower a the bad guys "control" over the area by doing raids, defending against raids, doing missions...and most importantly (to me), destroying structures.

You can destroy them at your leisure, and by whichever means you'd prefer, but there's nothing more satisfying to me than getting into a huge truck and crashing wildly into a huge building. It's not perfect, the story could be better, it can be kinda monotonous. But...if you kill enough bad guys with a hammer, you unlock a cheat where your hammer becomes wildly overpowered, and you can straight up Dragon Ball Z an APC through a building. It's glorious.