All the others : http://www.youtube.com/watch?v=lLimlcmdkSg
I haven't played Black and White 1, so I don't know from where does option eight come from, since I only know of the other two rivals, but it was in the video so I put it in anyway. Anyway, gotta go with Blue's theme from FireRed/LeafGreen, such a classic.
Brendan/May's Theme Bianca's Theme Blue's Theme from Pokémon Red, Blue, and Yellow Hugh's Theme Rival's Theme from Pokémon Black and White (???) Barry's Theme Silver's Theme from Pokémon HeartGold and SoulSilver Cheren's Theme Blue's Theme from Pokémon FireRed and LeafGreen Silver's Theme from Pokémon Gold, Silver, and Crystal
I love the upbeat peppiness to encountering your rival in RSE. The fact your Hoenn rival was more like a friend than a rival probably contributed to its sound. Still, I fancy it the best. Bianca's theme is also uplifting, and another close favorite.