I no longer remember the exact boss or who was raiding with me, but I do clearly remember having a conversation with a friend while I was healing Karazhan. At the time, I was grumbling that I didn't think we had the right group composition to do an encounter successfully -- but it was only after the group's other healer died that my friend agreed. Of course it was then that I decided this wasn't going be a wipe -- something I hadn't thought was possible until just then. (Certainly no one was more surprised than I was when I pulled it off.)
Whether raiding or not, we all have close calls in game -- that was only one of many I've had. But it was certainly memorable. So what about you, dear readers? Share your stories, your near-misses, your especially memorable almost-but-not-quite deaths.