I'd say that it wasn't a particular band per se, but more of a movement...and I'd call it the Lollapalooza decade, even if Lolla only lasted 7 years and burned itself out by 1997. Nirvana single-handedly created the footprint that would impact the decade commercially and musically, but it was Jane's Addiction that really started to draw over the metalheads to alternative music and that became important to how many records a band could sell, and Perry who brought the flood of "college" rock to the masses. (I'd love to know how many people bought Use Your Illusion and the Black Album, but also Nevermind and Core. I'm guessing quite a lot.) But most of the biggest bands of the decade played Lolla. Pearl Jam, Red Hot Chili Peppers, Nine Inch Nails, Smashing Pumpkins, Beastie Boys, Tool, Metallica, Soundgarden, Alice in Chains, Stone Temple Pilots, Green Day, Sonic Youth, Hole, Pavement...and there was also a representation of hip hop, which needs to be highlighted. A Tribe Called Quest, Ice Cube, Ice T, Snoop Dogg, and Cypress Hill. By the late 90's, pop was ruling again as well as nu metal. I can't really say that there was a Prince or a David Bowie, artists who constantly evolved and released record after brilliant record.
