There's no achievement for this (as far as we know, though if Blizzard is listening, maybe we'll see it in the next patch), but it's still awesome. A guild called You Are So Dead on Kael'thas decided to run the first annual Obsidian Sanctum Death Derby, in which they tried to make it around Obsidian Sanctum on mounts without dying. As you can see, it's quite a run -- they didn't aggro the middle boss until the very last lap, and the max run around without dying was about four laps (Paladins obviously had the speed and plate bonus, though a Warrior and a Mage also ended up among the winners, who all got 100g each).
Unfortunately, the video above was made with a cheap version of FRAPS, so as atomic645 says, you get all of the starts and almost none of the spectacular deaths. But they do plan to do the death race again (and maybe this is something you can try with your guild on the next OS run), so expect more video soon.