Kobu (Street Fighter 3 Third Strike)
Quiet and contemplative in the front half, firey and combative in the back half, just like our man himself. Not the traditional Ryu theme by any means, but it would be a disservice if it wasn't here.
Ryu's Stage: (Smash Bros for 3DS/Wii U)
It's the SFII stage we all know in love with traditional Japanese instruments and a sick violin solo, what else do you want?
Theme of Ryu: (Marvel vs Capcom 3)
I wouldn't consider myself a fan of dubstep adjacent music, but I put a thousand hours into MvC3 online play, and with Ryu as my anchor on a team with Captain America on it , I fell in love with MvC3s more electronic songs
Ryu (X-Men vs Street Fighter)
I love the Vs Series on the CPSIIs soundfont. That crunchy synth trying to mimic a guitar just works for the Street Fighter II compositions, and in general it sounds so good that they just remastered a ton of returning character's themes for MvC3.
Honorable mention
Ryu Theme (Street Fighter Alpha 2)
On the other hand, the CPSI soundchip is...trying its best. It can't quite mimic a guitar, so we just have a church organ and really loud drums just going ham. But you know what? I love it. It sounds great on an Alpha 2 arcade machine and that's all that matters
Theme of RYU Remix [Stage of AYUTAYA ISEKI] ~ Satoshi Ise (Capcom vs SNK)
This theme just screams 2000 to me. The lo-fi hip hop beat combined with vocal samples that wouldn't be out of place on a German techno hit of the previous decade. Just manfique, perfect. Play a 4 vs 4 on that purple desert stage from CvS and you'll see what I mean, you'll get lost in it.