Xbox vs Playstation, Sega vs Nintendo, Scorpion vs Sub-Zero, Penis vs Vagina, Sonic vs Mario, Jack Thompson VS Gamers, Peter Molyneaux vs The Truth, Spy vs Spy, but of course none can top RED VS DOUCHEBLUE!
I like as a rivalry..
Juto vs. Crocell
They have a good rivalry because while they are on the same side (most of the time) Crocell see's Juto as the new guy and tries to show that he is better. Of course, nobody really ever proves they are better even though we all know in truth Juto stomps Crocell all over the yard ^o^
Cain and Abel from Xenogears. The first man to arrive on the planet versus the first man to be born on it. The two beings who would go on to make contact with The Wave Existence and forever struggle against one another to achieve their purpose. A rivalry that spread over thousands of years and multiple incarnations of each individual. A rivalry that at times defined who each were, and drove their every action. Their story also acts as a powerful reimagining of the story of Cain and Abel from the Book of Genesis, full of religious symbology, and the complex account of the opposition they both faced made for a truly thrilling rivalry.
Blazblue: Ragna vs Jin
Guilty Gear: Sol vs Ky
Justice vs Kliff
Street Fighter:Ryu vs Ken
KOF: Kyo vs Iori
Soul Calibur: Siegfried vs Nightmare
Darkstalkers: Morrigan vs Dimitri
MK: Sub zero vs Scorpion
Starcraft: Protoss vs Zerg
Tiberium Series: GDI vs Nod
Warhammer: Space Marine vs Chaos Marine
Red Alert: Allied vs Soviet
FFVII: Cloud vs Sephiroth
QuakeIII: Doom vs Ranger