For now I'll just do Pokemon, since otherwise this would get insane. Though I'm sure people will declare me insane by the end of this anyway. >_>
R/B/Y:
Gym battle,
trainer battle, Team Rocket, Cerulean City,
Celadon City, Saffron City, Cycling Road,
Route 1,
Until We Meet Again...,
Game Corner D/P remix, champion battle,
Pokemon Center, St. Anne
G/S/C: Wild battle,
trainer battle (this is someone's MIDI remix, but close enough), instrumental version of Ready Go,
Azalea Town (non-MIDI remix this time)
R/S/E: Gym battle,
trainer battle,
Slateport City (however, instrumental or bust), Route 120 and 121 with their awesometastic music that almost matches Until We Meet Again, contest theme,
Regi battle, Advance Adventure ~faunsu e~,
Team Magma theme, Team Aqua theme, Battle Frontier,
Frontier Brain battle,
Deoxys battle
D/P:
Wild battle,
trainer battle,
Sunyshore City,
Hearthome City,
Galactic Admin battle,
Hikari's theme (but, uh, an instrumental version
),
Route 201, Wi-Fi lobby, GTS,
Fight Area,
Jubilife City,
Route 225,
legendary trio,
Route 210 (preferably more styled after the anime's orchestral version),
Route 209,
champion battle
Colosseum:
Miror B. or
Mirakle B.,
first battle/early Mt. Battle,
semifinal battle,
Phenac City (maybe only the fast part, but preferably both), The Under,
final boss theme (ignore the crowd cheering >_>), intro screen,
practically anything that had portions played in the ending theme
XD:
Cipher Peon battle,
wild battle (1:23), vs. battle (2:48),
Greevil battle,
Miror B. (disco influence this time),
purification chamber (might be a remix, but I'll take what I can get)
Obviously I'm not expecting even 15% of these, but I'm just saying: if they had to pick stuff, I hope it's selected from these. Ironically enough, I'm actually not a fan of the main theme that makes it into every Smash Bros. game... (Except for the more tropical version from D/P, but that's not in Brawl.)