Finding UFC fights on YouTube is something of a crapshoot. Sometimes highlight videos, like the one above, are posted by UFC. Sometimes full fights are illegally uploaded. Sometimes there's nothing.
But UFC.com has done something pretty cool: It posted the entire Hazelett-Burkman fight online. I just watched it, and it's a high-quality video with none of the bugs and glitches that often come with online video. If you haven't seen the fight, it's highly recommended.
Obviously, UFC is never going to post pay-per-view main events for free online, but posting undercard fights as a promotional vehicle makes a lot of sense. UFC is way ahead of the other sports leagues when it comes to online video.