In Guildwars (PC), players leave the newbie island via "The Searing," a cinematic which shows the savage destruction and subversion of the land of Ascalon at the hands of invaders. The landscape is changed to a fiery wasteland, and the humans have been pushed back into small and isolated forts and settlements.
Dark Cloud (PS2) starts with a cataclysmic event that imprisons everyone and their homes in dungeons around the world. Dark Cloud 2 reveals that the world outside your isolated hometown is barren and empty. In both games, the goal is to rebuild the world in some manner.
Actraiser (SNES among others) is a platforming/sim that gives you control of an angel (or was it God?) who has been tasked with rebuilding the world that was destroyed by his arch-nemesis in the prologue.
There is a shareware game by Ska Software called Survival Crisis Z, where zombies control the world. The object is to survive long enough to get an airlift out of town. You can help yourself survive by trading supplies from outpost to outpost, rescuing survivors, or conquering the city one outpost at a time. If you don't mind the dated graphics, it just might be right up your alley.Turns out this one can be downloaded for free at http://skasoftware.wordpress.com/category/scz/
There are even some games that give you the option of a "bad ending" where you have fouled everything up. Chrono Trigger has an ending in which, through your meddling in time, a species lizards became the dominant life on earth instead of humans.
Dead Rising (XBOX360) is a Zombie-Horror type game where you control a photojournalist trapped in a zombie infested mall for 72 hours. Depending on how much information you uncover about the zombie problem, the endings can be apocalyptic.
Deus Ex (PC, PS2) is a highly-acclaimed first-person shooter/adventure game that draws heavily from conspiracy theory lore. Without spoiling too much, at least one of the endings involves messing the world up pretty good.
Lastly, light guns? If you want some good peripheral action, look for House of the Dead, or better yet, Typing of the Dead.