Irenic recently reached level 90 in Mists of Pandaria with a grand total of zero creatures killed, 92 total damage done, and one completed quest. "The one quest I got is a new unavoidable quest that is now auto-flagged as complete for all factions. It registered after I hit 86," Irenic explains on WoW's forums.
How did he manage it without a single kill? "Since the entrance to Pandaria isn't designed to be entered without questing and killing, I spent all my time doing archaeology and gathering in Kalimdor," Irenic wrote.