Cloud's Theme - I didn't know Cloud had a theme ^^; Is there one? What is it?
Vincent's Theme - Unless it's from Dirge of Cerberus, I didn't know one existed. Or could The Nightmare's Beginning (song played in the ShinRa basement when you find him) be considered his theme? If so, it's a very cool song. Subtle, quiet, and mysterious, with also some lingering sorrow...definitely one of my favs, along with One Winged Angel and Aerith's Theme.
Yuffie's Theme - Makes me think of people skipping too XD Or penguins dancing O_O You know, with the top hats and canes? It's a chipper kind of song -- it always makes me feel cheerful.
Tifa's Theme - Always makes me feel at peace. It's very soothing and relaxing, and I like to play it on the piano when I'm feeling mellow.
Barrett's Theme - Bouncy is a pretty fitting word. Good tune, makes me feel brisk and like there's work to be done, but with a certain good-humouredness to it.
Red XIII's Theme - I love how this song is a rearranged version of Cosmo Canyon. The drums in this song are great, and I always think of campfires and Native American story-telling when listening.
Cait Sith's Theme - Hehe, this one makes me chuckle. I always feel a little mischiveous, sly, and playful when I listen to this song.
JENOVA's Theme - This one always makes me feel edgy, hyperactive, and a bit paranoid.
Sephiroth's Theme - Pretty much indescribable to me (it's that good), but it always gives me a thrill, as well as a sort of oncoming 'dun dun' feeling. Awesome song--I play it on my radio show all the time X3
Cid's Theme - Not one of my favs, but I still like this one. It makes me feel determined, like I have a purpose to fulfill.
Aerith's Theme - Words can't describe how much I love this song, especially the orchestra version. It makes me feel hopeful and extremely happy, like there's something to live for and that I'm not alone. But it also makes me feel a little sad because you can hear the losses and sacrifices that are imbued into the song.
And don't forget the...
Turk's Theme! - Although there isn't too much to it, it gives off a sort of feel that it's the definition of cool

Too cool. Hehe.