Street Fighter....
A game that has shaped an entire genre.
Without Street Fighter, as stated above, the fighters we have today like Virtua Fighter, Tekken, and Mortal Kombat would never exist.
Capcom may not even hop into the Capcom vs. Series, as the idea was more "Street Fighter vs. whomever".....
I could see a bigger emphasis on Mega Man. Perhaps Mega Man would continue as a respected Platformer, and not have games announced, then cancelled a few months from release, like we've been getting.
The Dreamcast (if it still exists) would probably die earlier, Marvel vs. Capcom 2 is still considered best on the Dreamcast in a lot of circles, and for a while Capcom was the only major 3rd party developing for SEGA's last hurrah.
Also, Mortal Kombat can be seen as a major turning point in the 16-bit era.
Nintendo censored the first game, SEGA didn't.
Initially this helped SEGA quite a bit, but Nintendo brought it up, and that's how the ESRB formed (in a nutshell).
This established Nintendo as the Child-Friendly console. That made it a lot harder to sell consoles. Back then (as it is kinda of seen today), Kids were the primary audience of games. Parents aren't going to go out and buy the console that will expose them to *gasp* VIOLENCE AND GORE!!
Without MK, Sega may have more leeway, and it may even prevent the hasty planning that was the Sega-CD and 32-X, and the abandonment of the Saturn.
Just the first few thoughts at the top of my head.