Kairi has three theme songs and of the three, "Kairi III" is just... beautiful. Like music from heaven in its purest form... It's nostalgic, sad, and heartwarming. Kairi's other themes, "Kairi I" and "Kairi II" are just as beautiful.
The PLANITb Remixes of "Hikari" and "Simple and Clean" take the aforementioned songs and remix them into a different kind of awesome.
And then there's the version that plays during an emotionally dramatic scene in Hollow Bastion.
"Dearly Beloved", which is most certainly the real theme song of the series. The kind of music that takes all your worries away. Then there's "Dearly Beloved II", which is played during the final cutscene in Final Mix.
"Destati" and its variation "Dive into the Heart -Destati-", one of the first songs heard in the game. The music for "End of the World" is another mix of "Destati", complete with chimes, strings, and vague chanting in the background...or just vocalizations. There's a bit of vibraphone in there too. The effect is both beautiful and nightmare-inducing.
Destiny's Force is the theme used for very powerful bosses. It does its job at making the player feel like they're dealing with something powerful. The theme itself is also very intense, and uses its instruments very well.
"Another Side". Plays in the Final Mix secret ending trailer, and it spawned "Organization XIII", "Graceful Assassin", and "Showdown at Hollow Bastion". A remix of the whole track was used in 358/2 Days, and the actual track was used in Aqua's battle against Braig in Birth By Sleep.
"Night of Fate", very fitting for the night that kicks off Sora's adventure with the Heartless' invasion of Destiny Islands. It's also Traverse Town's first battle theme, before you meet Donald and Goofy. To add more epicness, try to listen to it when you're inside a room while there's a storm outside.