I've not noticed this before and I feel like it might be new, but the fine folks over at the NCAA have put some full games from past NCAA Tournaments on YouTube. In their NCAA On Demand channel, there is a section labeled NCAA Vault. They basically include the Sweet 16 games through the title game from what I can tell, with a few of the major upsets sprinkled in there. The latest it has uploaded is 2011, so the Bobcats 2012 Sweet 16 run isn't in there, nor is the upset of Georgetown. Womp, womp... :(

It is a pretty enjoyable tool, though. I got some entertainment out of Steph Curry's 40-point barrage of Gonzaga in 2008 and needed some background noise so I listened to a couple of Xavier games.

https://www.youtube.com/user/ncaaondemand