2013 was a very light year in gaming for me as I had other priorities - my daughter was born! I never actually finished this list and didn't even really have 10 worthy games. I have since had more time to catch up on gaming, and finally finish this list at the end of 2014. There are a few caveats - two of these games, I did not actually play until 2014: Tomb Raider (via definitive edition) and Guacamelee (via Super Turbo edition), and Rogue Legacy (via Vita release). There are a few other notes that you can find in the honorable mentions or in the comments for each entry.
Diablo 3 - As I am finishing this list in late 2014, I'm going to use my time traveling abilities and make an easy cut of Diablo 3, as it is highlighted as one of my 2014 GOTYs in this years list via the Ultimate Evil Edition.
Rogue Legacy - I finally got around to playing this via the 2014 vita release. What a great game for that platform. I had tons of fun making runs through the castle and upgrading like crazy, but after so much work I had only conquered a couple of the bosses and I have to admit that each subsequent run started to feel very grindy. Still, a very fun and unique game.