Official themes for each class.

[SuperYay]

Most of the themes are pretty obvious but I'd say there's a few up in the air.

Scout - Faster than a speeding bullet
Soldier - Rocket jump waltz? Art of War? Both?
Pyro - Dreams of Cruelty
Demoman - Drunken Pipe Bomb
Heavy - ??? Does he have one or did I miss that? I think his is supposed to be the main theme, it plays at the end of his trailer, but I don't think he has one for him specifically.
Engineer - More Gun
Medic - Archimedes? Little heart to heart? Medic!? All three?
Sniper - Magnum Force
Spy - Right Behind You (Also maybe Petite Chou-Fleur, and I think Dapper Cadaver fits him well)

[Fliby]

Just watch the "meet the team" shorts.

[Krenesh]

Demo
https://www.youtube.com/watch?v=SjtyGDOPgRw