Probably bad film: 2012 (2009), starring John Cusack, Chiwetel Ejiofor, Amanda Peet and others, directed by Roland Emmerich, in which the world is devastaed by natural disaster. To be honest, the name of the director alon is enough to deter me from wanting to see this.
Possibly better film: Time of Roses (1969), original title Ruusujen Aika. Summary from here: "Taking place in the year 2012, the film is a fantasy of a "utopian" time when all class conflicts have been erased, at least superficially. A history researcher Raimo Lappalainen becomes obsessed by the life of nude model Saara Turunen, a woman who died in 1976, and tries to reconstruct it for TV, with help from an actress. At the same time a strike in a nuclear plant will lead to a violent upsurge, which media only manages to keep secret from public with a clever cover-up." See New York Times review, and some pictures.
Comics: Bloody Mary (1996-7) by Garth Ennis. Concerns Corporal "Bloody Mary" Malone, an American commando, who in one story must raid a fascist-ruled Europe and in another must assassinate a religious tyrant ruling New York.
Radio: Deep Trouble (2005, 2007), a BBC sitcom set on a nuclear submarine. This one does look like it might be worth tracking down.
Robert Silverberg novels: Silverberg has written so many novels that it's hardly surprising that more then one of them is set in 2012. I had heard of the first but not the second. Descriptions of plot from SF Encyclopedia.
Shadrach in the Furnace (1976) - "concerns the predicament of the personal physician of a future dictator who finds his identity in jeopardy." Nominated for Hugo and Nebula.
The Second Trip (1971/72) - "an intense psychological novel describing the predicaments of a telepathic girl and a man whose Identity has been newly created in the body of an 'erased' criminal."
Television: The mainstream school of thought on Joe 90 is that it is set in 2012-13, though apparently there is a minority faction who support 1998.
Doctor Who TV episodes:
Dalek (2005, Ninth Doctor) - set in an underground base in Utah, before this year's presidential election
Fear Her (2006, Tenth Doctor)- set during the Olympic opening ceremony in July.
Other Doctor Who stories set in 2012:
Frozen Time (2007 audio, Seventh Doctor) - frozen in the Antarctic ice, both a mysterious blue box and also other things you often find frozen in ice.
Christmas on a Rational Planet (1996, New Adventures novel by Lawrence Miles) - parts of it sert in Arizona in 2012, though the main dated chunks of narrative are in 1799.
Relative Dementias (2002, Past Doctor Adventure with Seventh Doctor) - first chapter set in London in August 2012, rest of story in 1982.
The Shadows of Avalon (2000, Eigth Doctor Adventure by Paul Cornell) - the Brigadier becomes embroiled in conflict over a dimensional gate to the parallel world of Avalon.
NB that the Seventh Doctor appears to have visited this year at least three times, his successors once each (excepting the Eleventh Doctor for whom this year is contemporary) and his predecessors not at all.
Recommendations and additions to the list very welcome.