WARNING: Per wiki policy, Spoilers Off applies to Awesome Music pages. All spoilers will be unmarked.
"Memories in Pieces", the opening theme which has bits from "Hand in Hand", a chilling version of "Scent of Silence", Naminé's beautiful theme, and then the ominously awesome "Castle Oblivion".
"Naminé's Theme". Much like Kairi's Theme, it's so beautiful. It also uses something similar to "Prelude" as a background tune.
The Re:Chain of Memories version of "Sinister Sundown", for your daily dose of great fight music. And it's a good thing it's so good, because you hear its Kingdom Hearts II incarnation a lot in Days...
"Forgotten Challenge", especially the Game Boy Advance version. It's actually a pretty good use of the Game Boy Advance sound technology. If you listen closely, the percussion has the same rhythm as "Destati".
"Night of Fate" is the battle theme of Destiny Islands and acts as a musical accompaniment for Sora's sadness, confusion, and drive against the Heartless until he comes to understand himself and his power....on the night when all this happened, no less. Creative name. The Re:Co M version in particular adds something new to it. It replaces the driving metallic clanging Brake Drum and the driving strings in the second part of the main melody with Claves and Saxophone. This gives the song a more island-y vibe, as the Claves sound like water drops. Fitting for how in Re:Co M, Night of Fate is ONLY Destiny Island's battle them, while in other games, it's used in other places as well.
"Revenge of Chaos, the rather underrated theme for Riku's final battle against Ansem.
"The Force in You", which incorporates parts of Ansem's themes from the previous game to create a tense battle theme for Riku Replica. Good thing it's so awesome, too, since players will hear it quitea lot.
On a more light-hearted note, there's the minigame theme "March-A-Long", and the more fast-paced "Dash-A-Long". "March-A-Long" also gets re-used for the "Hunny Pot" Command Board in Birth By Sleep as well.
"Simple and Clean" by Utada Hikaru is an awesome but also heartwarming song that makes you feel good inside.