Cities are often the targets of wars, terror plots, demonic invasions and other such perils. The result will almost always lead to the city being completely trashed, with buildings tumbling and/or on fire, debris in the streets and death all around.
A city most often shown in ruin is Berlin circa 1945, ravaged by Allied mortar and bombing attack by the climax of many World War II-based games. A more recent example of a ruined city is Pripyat, which was simply abandoned after the explosion at Chernobyl reactor four and has since fallen into severe disrepair. City 17 has similarly gone into disrepair as the Combine and Administrator Wallace Breen are more concerned with the exploitation of humanity than preserving its cities.
Most cities are, however, ruined quite suddenly. Kvatch is overrun by Daedric forces after the opening of an Oblivion gate nearby. London is reduced to ruin as the Chimera ravage England prior to the start of Resistance.
Then of course, there is Auburn, which is the unfortunate city at the center of the F.E.A.R story, destroyed in the explosion of a secret Armacham research facility, then has a war between two sets of mech-wielding soldiers, and finally is besieged by monstrosities as Alma's contractions mark the birth of a new, more potent member of the Wade family.
There are, of course, many different examples, but ruined cities are a mainstay of video games. They can provide tight environments with plenty of cover for difficult firefights, but can also lead to many similar, indistinct environments, and are thus of mixed value in most cases.