Weezer, definitely. Smashing Pumpkins ... eh. Probably, though it just doesn't seem like they were around all that long.
Otherwise, it's hard for me to separate the early 1990s from the 1980s.
The Offspring were pretty big for awhile. Beck had a huge amount of buzz going and some fantastic albums. Soundgarden should 100% be included.
Jane's Addiction, too, for their influence.