I'm gonna be that guy and tell you that Sail by AWOLNATION is not a 2013 song (but if you've discovered it in 2013, I guess that still counts).

In a similar fashion, my favorite song of 2013 is a song from 2012 that I discovered a few weeks ago.

I discovered ZZ Ward thanks to a small clip of this song playing during We're the Millers and I've been hooked ever since. Her whole album (Til The Casket Drops) is excellent.

If I have to go for a song released in 2013, I'd go with Despair from the Yeah Yeah Yeahs' (from the album Mosquito):

"Giorgio by Moroder" by Daft Punk

http://www.youtube.com/watch?v=5m4ZkEqQrn0

Answers is not some years old? I thought they used that song when they announced FFXIV.

Anyway I go with Stromae:

http://www.youtube.com/watch?v=S_xH7noaqTA

That's seriously deep.  Easily my favorite in this thread.  Second would be gamechaserbe's.

This guy makes the most interesting videos. Have you seen the one for Tous les mêmes?

Thanks, i didn't even think about it.  It's the song i liked the most this year. 

Giorgio by Morodrer in the new Daft Punk alblum RAM

Changed title from "What's your favorite song from 2013" to "What was your favorite song in 2013"

Lana Del Rey - Young and Beautiful
http://www.youtube.com/watch?v=RgKI7lubTj8