About "Here Comes Char", the song's lyrics are open to some Alternate Character Interpretation which makes it outright hilarious if you think of it as being sung by someone who got owned by Char.
Andrew W. K. also did a suitably awesome English version of Here Comes Char!.
We later get Oblivion from the same source as Men of Destiny. It uses the exact same instrumental, but rather than simply dubbing the lyrics into English, new somewhat apocalyptic, yet still awesomely GAR, lyrics were written, effectively making it a new song. Also somewhat unique for an English song, it was used in the original Japanese version of the show, and has perfect grammar and pronunciation. And it is freaking awesome.
Assault Waves, the perfect music to have epic MS duels to.
Char's Counterattack had an amazing orchestral soundtrack, rivaling anything coming from major American productions. Especially notable are "Main Title" and "Nu Gundam", and ends with an excellent, although non-orchestral song by the name of "Beyond the Time"
Fans are disappointed for many reasons that Crossbone Gundam has never been made into an anime... the kind of music the Crossbones get in video games is oneof those reasons.
Last Impression from Gundam Wing. What starts out calm turns out to be very upbeat, classical and... AWESOME. A fitting end to the AC Saga. This editor believes that lately this song is always the song for Gundam Wing characters when they appear in Super Robot Wars for a reason. It kicks ass.
"When the Dragon Swims, The World Ends" in the first episode where they introduce the Gundam pilots, and pretty much any song that uses Heero's motif.
"Zechs Comes"... too bad only bits and pieces of it ever got played in the series.
TWO-MIX in general is pretty good. Their other three Gundam Wing theme songs (Just Communication, Rhythm Emotion, and White Reflection), while arguably not quite as awesome as Last Impression, are all excellent in their own right. Check 'em out before Nabiki overcharges for them.
The "Just Communication" Instrumental: Played over the dub credits. The closest American viewers ever got to seeing/hearing the original TV show openings.
Use the Cloak of Darkness, most memorable for the scene where Duo jumps a bunch of OZ mooks with the Deathscythe Hell. Much reaping ensues. "THE GOD OF DEATH IS BACK FROM HELL!"
Treize's Theme, Man Who Makes History, gets a vote from this troper. Epic character gets equally epic theme music. And the first minute or so of "Enforcement Rush" gets special mention for being particularly badass.
Really, all that needs to be said about Wing's soundtrack is that it was done by Kow Ohtani, the award-winning composer behind ICO and Shadow of the Colossus.
And then there's this fandub of it. It's arguably even better than the original, if that were even possible. "Remaining 10% is worth dying for", indeed.
PRIDE (the second opening theme) by HIGH and MIGHTY COLOR. Hell yes.
Life Goes On is also filled with awesome, and has more variations used in the episodes than the other ending themes, I seriously counted at least 6 on the soundtracks. Kimi wa Boku ni Niteiru is also excellent, and is the only ending theme to be used in the series and the Special Editions.
Sakebi to Gekitetsu, played as Athrun and Mu race to destroy the Requiem. The finale of Destiny doesn't measure up to the one in SEED, but the music for it certainly does.
Gaia x Chaos x Abyss, the theme for the Extendeds early on in the show (coincidentally, this is when they're legitimately badass).
Launch! Impulse is a majestic theme for a Gundam launching sequence. It is reused as one of Shinn's themes in SD Gundam Generation Wars.
Kira, Just As He Pleases. Kira may have taken some actions during Destiny that were questionable, but his theme music is unquestionably badass.
No matter what you think of Lacus Clyne during Destiny, you cannot deny that Fields of Hope is one of the most beautiful songs ever featured in a Gundam show.