We had a kill in ICC, I forget which but it was either Festergut or Rotface, where only one person was left alive: a Hunter who had popped deterrence and managed to just barely finish off the boss.
Our first Blood Queen kill was also a near wipe, we had nothing but a Shadow Priest left up who lived via Dispersion(or whatever it is that reduces their damage taken significantly).
ICC 25 Normal with my guild... Progressing on Festergut. We got him to 3 HP and wiped -.- Not 3%, not 3k, quite literally 3 HP. Killed him next attempt, but seriously!!
The closest i've ever participated in was our first kill on will of the emperor and garalon, both on my warlock. tanks died, bosses came after me (soul shattered) boss goes after raid, kills them, comes back at me, dark bargain used, killed boss then died to millions of damage per tick, and garalon was on his enrage slam (he despawns seconds after its used) but i was last man standing and managed to kill him before he had a chance to escape.
progression raiding back in WotLK, died on blood queen, ankhed back up right when she killed the last person, she was charging me and she died from dots.
A few weeks after MoP Launch i had a pug raid and we literally kill-wiped the first boss. We were dead. The Boss was dead but despawned and we got an ID. Got the loot via mail a few days later. Never had that happening in like 7 years of wow .
First heroic Jin'rokh kill on 25. Me, the other tank, and 1 healer were alive and he was at 3-5%. Healer died from I believe a lightning ball and it was just us tanks left. With crazy taunt swapping to deal with lightning balls and crazy DK and monk self heals, we killed the boss.
Princess Huhuran in AQ40, we died when she was sub 1% and she starts flying off, she dies from DOT ticks. Turns out a rogue was AFK at the entrance and she was going after him when she was killed. It became a long standing joke in the guild. (Of course if he wasn't AFK, we wouldn't have all died anyways, but then it wouldn't have been funny)
Anub from Naxx when it was first out. Everyone of us was dead on the ground he was at 0% and the standing hunter shot off the killing blow as he was killed.