Before we had the luxury of enjoying Gust's games, Atelier Viorate had one of the most calming songs for a hometown ever: "Carrot Town's Number One Daughter"
Crystalized (yes, only one l) has 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 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.
"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.
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? If that's not awesome, then nothing is.
Allthreeparts of "Sublimation". Now that's some awesome final boss music.
From Ar Tonelico 3, there's "EXEC_COSMOFLIPS/", which is one of the most epic video game songs ever written.
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.
"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 The 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. The song is very likely making fun of you for losing, given the game it's from.
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.