It'll probably go to Log Horizon, as that's what I'm enjoying the most.
Honorable mentions, that I've enjoyed for one reason or another:
Magi: The Labyrinth of Magic, great shounen.
Valvrate the Liberator, great what the fuck are you doing(in a good sense) series.
The World Only God Knows: Goddesses, the continuation of an interesting series.
My Teen Romantic Comedy SNAFU, an interesting take on a school SoL.
Another noteworthy one would be Mayou Maou Yuusha. It was good. However, I kind of didn't feel like actually watching it to the end and while the story and the world and all the other little things seemed quite good, it just didn't have enough of a "pull" for me to finish it.
These are the only shows of 2013 that I've enjoyed from start to finish, or to 11th episode in Log Horizons case. Every other show of the year had me go "What aaaaaaaarrrrrre you doing?"(In a bad sense)