Godspeed You! Black Emperor is my favorite post-rock band and quite nearly one of my top 10 favorite bands.

My favorite GY!BE tracks include The Dead Flag Blues (that monologue at the beginning... haunting and beautiful), Storm (love the epic drum-driven intense section in the middle, and the frighteningly sad "Cancer Towers" part), and Rockets Fall on Rocket Falls (IMO their best straight-up song, and the one that got me into them).

As for other post-rock bands that kick ass, Explosions in the Sky (not just for noobs! Ryth is perpetuating a sentiment I'm not fond of), Port-Royal (EVERYBODY who likes any kind of post-rock or electronic music, please listen to Flares), Slint, Talk Talk, Mogwai, Tortoise, A Silver Mt. Zion (early stuff), Mono, 65daysofstatic, and Russian Circles are all top picks. Though the scene in the last few years has been utterly clogged with too many clones of Mogwai, GYBE, and even EITS (who themselves are very closely inspired by Mogwai and GYBE), so it's harder to find the stand-outs these days.