Awesome list @MF and Burnsy! Some great ideas on stuff to check out, thanks.
I wanted to throw out a few stand outs for me, not necessarily the best of the year and in no particular order:
John Grant - Pale Green Ghost
Grant's open disclosure is almost uncomfortable at times, but even in the depths of his despair the music is captivating.
DRENGE - DRENGE
Ruthless rock'n'roll with an edge. This two piece rocks.
Hevig Molledstad Trio - All of them Witches
Hedvig Mollestad Thomassen is simply amazing. This is Jazz that I can't get enough of. Possibly not as strong as Shoot! it's still a great example of Hevig's heavy style.
Suner McKane - Slect Visual History
Fantastic moody album recommended by @Rythm Devils.
Lorde - Pure Heroine
I tend to shy away from stuff that has gone main stream popular, but I'd be lying if I didn't admit that this one got a ton of listening time form me in 2013. It was my go to disk in the car.
Savages - Silence Yourself
Brilliant riffs and a great energy keep me coming back to this one.
Bombino - Nomad
This guy is crazy good on the guitar.
Blood Orange - Cupid Deluxe
This guy gets whats hot and does it right.
And a few others that have been mentioned, or get mentioned a lot anyway...
Vampire Weekend, Modern Vampires of the City
Waxahatchee - Cerulean Salt
The National - Trouble Will Find Me
Earl Sweatshirt - Doris