Aside from the immortal Street Fighter II and the clever (in a "Die Hard is my favorite Christmas movie" kind of way) Super Puzzle Fighter II Turbo nod, Street Fighter III is probably my favorite in the series. The number of unique animations, the art style, the famous Daigo parry that I saw before "esports" was a phenomenon observed by everyone from ESPN to HBO to university.
It was a bold move, leaping far flung into a new chronology of stripping it of most of the familiar faces that make up a typical Street Fighter roster (only Ryu, Ken, and Akuma were present before Third Strike brought Chun-Li back). It also might not have been a great idea for the series as a whole. It'd be a decade before the Street Fighter IV resurgence.