In Heroic Zul'Gurub in Cata, it wasn't so much an almost wipe as it was a moment of pure epicness. My brother was a Ret. paladin and I was an Unholy dk. On the first boss (the venom guy) the healer, tank, and other dps died during the poison maze. The boss was at about 70% health. My brother and I kept on fighting after everyone told us to wipe and we eventually killed him. Probably should mention gear wise we only had dungeon epics, the main thing was we avoided all the poison and managed interrupts really well.
Meh, don't know how impressive that actually is but it did make me feel like a boss at the time.