Haruhi Suzumiya: The most awesome episode is episode 12, Live Alive. It feels like the entire season is a build-up to this episode, and they finish it with Concert Climax and showing Haruhi's Character Development very nicely when she is helping the band, and her reaction after getting praised is priceless. Bonus points for her singing God Knows with freakin' Yuki Nagato on the guitar.
Episode 11 is perhaps the turning-point at which this becomes a great series. Keiichi, the likable protagonist, is contemplating murder, and we can't help but sympathise. His dilemma is very well portrayed, and the atmosphere throughout the episode is beautifully created.
Cowboy Bebop's Ballad of Fallen Angels. There are many outstanding episodes in the show but this one takes the whole cake. It builds up the tension so well; the dialogue, the atmosphere, and of course, the climax. It's CB at it's finest and I always get goosebumps whenever I rewatch it.