Perhaps the best way to see the influence of Street Fighter II in early-to-mid-'90's gaming culture is to look at the other fighting games that sprung up overnight. Capcom is, of course, almost directly responsible for the rise of SNK, who made a longterm business from 2D fighting games. And Mortal Kombat is most assuredly a direct response to Street Fighter II, adding features the latter omitted, like ugly digitized graphics, over-the-top violence, and Claymation.
But of all the copies, derivatives, and clones, the most clone-like may just be Data East's Fighter's History, otherwise known as "The game that Capcom tried to sue Data East over."
Capcom saw Fighter's History as, well, uncomfortably similar to their own Street Fighter II. Uncomfortably, infringingly similar. That's why, in 1994, Capcom filed a motion in a California district court to prevent Data East from distributing Fighter's History arcade machines. They were able to prove that SF2 was a significant influence on History by referring to Data East's design documents, which were rife with references to Capcom's work. They were unable to prove, however, that the characters had been copied directly, and thus lost the lawsuit. Capcom's loss (and, really, they only lost legal fees here, because nobody in their right mind bought or played Fighter's History instead of SF2) was our gain, as Data East released the SNES version of the game that same year. Data East was then free to continue the series, with Fighter's History: Mizoguchi Kiki Ippatsu! and Karnov's Revenge/Fighter's History Dynamite.
Luckily, by sticking so close to the source material, Data East accomplished what most second-tier fighting games could not: decent controls. It was actually possible to play the game, pull off some special moves, and have a basically okay time, unlike something like Ranma 1/2 Hard Battle. Most people focus on the ripoff aspect, and miss that Fighter's History is a not-awful fighting game.
Fighter's History bests Street Fighter in a way that Street Fighter can never outdo, unless they buy the rights to Data East's characters like, uh, SNK has: Karnov. The bald, portly, fire-breathing Russian strongman who was something of a Data East mascot appeared as the final boss in this game, doing what he did best: breathing fire. He was outfitted in some desert headwear, presumably so the player would have something to knock off other than his pants. FH featured a system in which specific accessories could be knocked off of fighters after sufficient damage, triggering a dizzy.