My DM wants me to pick a couple of backgrounds for my character for a 4e game. Where can I find them?
One good source is the "Backgrounds section on this page. It lists major sources and summarizes the mechanical implications of the backgrounds.
DDI Character builder has a complete list and the demo is free.
Many backgrounds are specific to a particular setting. So the Forgotten Realms Player's Guide, Eberron Player's Guide, and the Dark Sun Campaign Setting each have a set. If you're playing in a particular setting, ask to borrow the campaign guide to get access to the list. That's probably the easiest route.
The various X Power books (Martial Power, Primal Power, Psionic Power, etc) include backgrounds relevant to the book's focus. The Player's Handbook Races: X books (e.g. Player's Handbook Races: Dragonborn, Player's Handbook Races: Tiefling) have backgrounds relevant to those races. There are also some in the Player's Handbook 2 and 3, as well as the
Going through all of those books is difficult. Many people use Dungeons & Dragons Insider to get the information, where it's all collected in one place. If you have a D&D Insider account, the DDI Character Builder and the D&D Compendium both offer a nearly complete list of backgrounds and will note which book they are originally from. DDI is a bit expensive, so if you don't have an account, see if your GM does and ask to borrow him computer for a bit to browse the compendium.
Finally, if all of that is too complex, I recommend just telling the GM you want the Akanûl background from Forgotten Realms. +2 resist cold, fire, and thunder. Hard to go wrong with that. :-)