Capcom vs. SNK
Rumor has it (and by rumor, we mean Wikipedia) the Capcom vs. SNK (or SNK vs. Capcom, depending which company developed the particular game) series originated when an issue of Arcadia Magazine featured the headline "KOF vs SF," or King of Fighters vs. Street Fighter, on its cover. Assuming it was a mash-up of the two series, fans were enraged to open the magazine and find they had misinterpreted it.
Noting the demand for a collaboration, Capcom and SNK then teamed up to release several fighting and spin-off games featuring their respective characters beating the piss out of one another (and in a few instances, playing cards). We'll never get tired of watching Chun Li and Mai Shiranui together on the same screen, so here's hoping for an eventual third entry from Capcom.