There are many game titles, throughout the years, that have included environments that are destructible to variable degrees. Some games, such as Red Faction, have fully destructible environs, in which everything can be destroyed, (buildings too!), thus adding a greater fun-factor for some players, although it can be a little hyper-realistic!
While other games, like Diablo 3, have only partially destructible environs, allowing players to only destroy particular areas/assets in the game that allow them to, either find loot, or proceed through a level.
Giant Bomb has an awesome listing of games with destructible environs, which they keep up-to-date. To see the list, click here.
