The following are links to free guitar tab and audio for some of the most popular songs in 2011.
Here's the tab from their 2010 album Sigh No More. The song uses the unusual tuning of EACGCE, which essentially amounts to an open Amin7 chord. Additionally, the guitar uses a capo on the fifth fret. Includes links to Spotify for audio of the song.
Okay, so Bon Iver's "Skinny Love" wasn't on his 2011 award-winner Bon Iver, but this was nonetheless one of his most popular tracks from 2007's For Emma, Forever Ago. He interestingly tunes his guitar to GCEGCC on this song, which results in an intentionally small, thin sound guitar sound.
This track from 21 a pretty straightforward one, as far as the guitar part is concerned... you'll just need to make sure your palm-muting technique is good, and the rest is a piece of cake.
Tons of energy on this song from 2011's Wasting Light, which makes "Bridge Burning" an absolute blast to play! The post includes links to Spotify so you can play along as you listen to the original recording.
This is definitely not a "guitar song", but fans of the more recent-vintage electronic Radiohead will probably have fun mimicking the synth parts on guitar. "Lotus Flower" is from 2011's King of Limbs.
If you're looking to learn an instrumental song that all your hipster friends will recognize, this track from Fleet Foxes 2011 record Helplessness Blues should fit the bill. Some nice "classically inspired" bits to learn on guitar here.