Equally awesome is her rendition of the second season theme song, Super Driver.
Tchaikovsky's Symphony #4 Movement 4 from the climax of "Day of Sagittarius III" and Mahler's Symphony #8 Part 1 from the climax of the first season. Both of them are also awesome outside of this context, naturally, but this is where they accompanied Crowning Moments of Awesome.
Also the piece that played during the battle, Shostakovich's Symphony No. 7 'Leningrad', The Invasion.
Haruhi herself gets a particularly rockin' one with the piano-and-guitar-driven "Parallel Days", Tsuruya-san shows off her cute voice with "Seishun Ii Janai Ka", which stands out with a great Chinese string section, and Itsuki's purring sex of a voice translates to music with the fun, earwormy "Maggaare Spectacle", which also has little voice snippets from Yuki and Mikuru!
You may not care about the character much or even remember her. But Emiri's Fixed Mind is gorgeous and heart-touching.
One of the best songs in the soundtrack is also one of the simplest: Itsumo no Fuukei, which translates to "Everyday's View". It's known for being that piece of music heard when Kyon talks about no longer believing in aliens, time travelers, and espers in the first episode (in chronological order; it's the second episode in the other order).
Suzumiya Haruhi no Gensou is essentially a concert of songs from the anime turned into classical music (and also very, very awesome). A few songs have already been mentioned on this page, but listen to the version of Lost My Music to be completely blown away.
The Russian versions of the first season's songs are quite amazing too.