The answers are all pretty good (I've put them all behind the break -- thanks, Twitterers!). From what most people said, lore and story play a huge part in making a fight feel epic, and not just the story of the game, but the story of the guild playing as well -- when your guild almost wipes, and pulls off a great kill, that's an epic battle whether it's in Karazhan or in Sunwell Plateau. Challenge also helps -- people raid to be pushed to the edge of their endgame abilities, and when a well-tuned fight does that, it's one of the best experiences in the game.
Great answers all -- hopefully we'll get to see more epic encounters than not in the Wrath of the Lich King (as Matticus points out, we don't need 40 or even 25 players to have a truly epic encounter with Arthas). And if you haven't started following our Twitter account (@WoWInsider) yet, please do, and stay tuned for more interesting and informal Twitter polls like this.
lipinski77: Epic encounter: Downing a new boss after 1 wipe with no deaths. Also, all the drops are needed, no DE necessary.
pkdan14850: A fight that the players never know for sure they are going to win until the very end, with all power bars low when they finish.
danielandlions: an "epic" encounter has a large scope. Karazhan feels epic when you're in blues and wiping to learn it. Molten Core felt epic because it took 40 of us. BWL and Naxx the same.
admiraljustin: I'd imagine it is: no matter how good you became, or how scripted the actions, you do something amazing that you can't repeat.
shinmeko: What makes an encounter epic is the skills and grandiose feel the fight imbues the player with. Talent + respectable challenge!
ipwn: a combo of lore, strategy and presentation. Epic: Mags, Vashj, Leo. Nonepic: BM (no strat), Rokmar (no lore), VR (boring pres)
JohnNewsom: I'd consider something to be epic if it produces a good story. Even a wipe can be epic.
isheepthings: the raid/encounter is epic if I am moved to mute vent and turn up the game sound to hear the boss monologue.
danielwhitcomb: Good Lore, Menacing feel to the boss, and clever mechanics to the fight.