My list, in the format of rivalries.
Megaman vs. Sonic
Zero vs. Shadow
Ryu vs Akira (Virtua Fighter)
Chun Li vs. Sarah Bryant (Virtua Fighter)
Haggar(Final Fight) vs. Axel (Strrets of Rage)
Poison(Final Fight) vs. Blaze(Streets of Rage)
Strider (Strider) vs. Joe Musashi (Shinobi)
Dante vs. Bayonetta
Morrigan vs. Tyris Flare (Golden Axe)
Arthur vs. Gilius Thunderhead (Golden Axe)
Felicia vs. Centurion (Altered Beast)
Akira Yuki (Virtua Fighter)
Axel Stone (Streets of Rage)
Beat (Jet Set Radio)
Gilius Thunderhead (Golden Axe)
Kazuma Kiryuu (Yakuza)
NiGHTS (Nights into Dreams)
Ryo Hazuki (Shenmue)
Sakura Shinguji (Sakura Wars)
Selvaria Bles (Valkyria Chronicles)
Sonic the Hedgehog
Ulala (Space Channel 5)
Vyse the Sky Pirate (Skies of Arcadia)
Zephyr (Resonance of Fate)
Arthur (Ghosts 'n Goblins)
Dante (Devil May Cry)
Date Masamune (Sengoku Basara)
Edward Falcon (Power Stone)
Frank West (Dead Rising)
Gene (God Hand)
Jedah Dohma (Dark Stalkers)
Kyosuke Kagami (Rival Schools)
Leon S. Kennedy (Resident Evil)
Mike Haggar (Final Fight)
Mega Man X
Ryu (Street Fighter)
Tessa/Tabasa (Red Earth)
Samanosuke Akechi (Onimusha)
Not really sure about rivalries.
I like to make PSASBR move-sets. Here's a few:
Never say I don't contribute: I'm The Idea Man.
I kinda like Konami vs. Capcom more, to be honest.
[or Marvel vs. DC, DC vs. Jump, Street Fighter vs. Mortal Kombat, Jump vs. Capcom, SMASH BROS vs. ALL-STARS lol]
= = Every day is Kill la Kill day!! = =
Mortal Kombat vs. Street Fighter
Out of all the crossover requests I hear, MKvsSF is by far the most requested. And for good reason, MK and SF are 2 of the most successful fighting game franchises to ever exist. And they were 2 of the earliest ones.
Marvel vs. DC would be cool, but only if it was made like Injustice. A one on one fighter, not a 3 on 3 fighter.