Also, Solitaire, which pretty much manages to turn any scene into a Tear Jerker.
Great Wilder (the Dark World theme), which also shows up in Disgaea and Makai Kingdom.
Thinking that it'd be a good idea to toss in Nefertiti and STIGMATA from Gust's Atelier Iris spin-off Mana Khemia here.
I'll be damned if Crystalized (yes, only one l) doesn't have an insanely catchy beat. And Disruptor is one of the most epic non-boss battle themes to exist (despite the undercurrent of slight melancholy...?).
Similarly, the first Atelier Iris game had a few pretty memorable but mellow songs toward the beginning, especially the City of Kavoc theme, but it was the last boss music that kicked an incredible amount of ass (especially since it had been hinted to musically at several points earlier in the game!) Japanese indie music demigod S.S.H. liked the song so much he felt compelled to make it even better.
Capping off Atelier Iris-related awesome songs, AI3 didn't have too many awesome songs in the game, but the opening song is made of JAM Project-level power-metal win.
And, of course, there's Laharl's boss theme (actually just a remix of Disgaea from the first game, which is an early indication that you are totally fucked.
And then, of course, there's Visual Sensation, which plays in the battles for the chapter leading up to the final boss. Very fitting, especially given that those battles are happening inside a mansion, and the tune has a very elegant feel to it.
Let's not forget Disgaea Rhapsody, which plays during the battle between Rozalin? and Laharl.
Sure, the music in the first Ar tonelico wasn't that great, but frankly, RE=NATION and Chronicle Key made up for it. The cutscene where these two songs are played are the moment that makes the game.
Ar tonelico 2, with generally better music brings us Replekia, a CMOA that you can bring out at your discretion, and Implanta.
METHOD_METAFALICA/. is arguably the best out of the three Metafalica hymms. EXEC_HIBERNATION/. also gets a mention for being a creepily epic ten-minute counting song.
Can't forget about Ar Tonelico 2's EXEC_DESPEDIA. Creepy vocals sung by the resident Dark Magical Girl Jacqli coupled with drum beats and guitar riffs and used as the background music for a battle with a giant robot? It that's not awesome, then I don't know what is.
Allthreeparts of Sublimation. Now that's some awesome final boss music.
This Troper feels the need to add Rustling Throb. It's the only song in a game to date that makes him want to not progress further if it means the music will stop.
From Ar Tonelico 3, there's EXEC_COSMOFLIPS/., which is one of the most epic video game songs this troper has ever heard.
Let's face it: any song on any of the Hymmnos Concerts has the potential to be a music of awesome. It all depends on a person's tastes and preferences.
Wanderer's Poem, arrange album version. Thank you, and good night.
Last World and DEAD END are also extremely awesome. (if you listen closely, you'll notice that DEAD END is actually a more dramatic version of Wanderer's Poem.)
Blue Concerto, especially the arrange version, which manages to be both epic and beautiful.
Nether Institute Evil Academy and A Song For You. Nether Institute Evil Academy is well-known for the dance number in it's opening, but the song itself is rather infectious and is reminiscent of A Nightmare Before Christmas, especially toward the end. A Song For You differs from most of the Nippon Ichi ending themes by being rather upbeat and broadway-ish, but that's what makes it one of the most memorable themes.
Makai Fugue. Best evil sounding song in the Disgaea series.
Also, the Maritsu Evil Academy Entrance Applicant Recruiting CM Song, also known as the game over theme. Never has there been a more chipper and bouncy song about the fact that you just got your ass handed to you. This troper wouldn't be surprised if the song turned out to be making fun of you for losing. Of course, given the game it's from, that's probably completely reasonable.
Phantom Brave has a very good soundtrack all around, but in particular, Violent Emotion and R&R Junkiee pretty much kick ass with a flourish, and Friend is exceptionally beautiful.
Speaking of Last Boss, we have the final boss music The Last Last Battle! Yes, it's your typical Ominous Latin Chanting final boss theme, but damn, it's too epic to not like.