Outside of some local metal/punk shows, the first 'big name' show I remember going to see was Lallapalooza '94. Smashing Pumpkins (who I don't even really remember) and the Beastie Boys (who tore the place to pieces) headlined. I don't remember all the bands we saw but the ones who stood out were Tribe Called Quest, Parliament Funkadelic, Nick Cave and the Bad Seeds (whom I had never heard of), the Breeders, L7 and Green Day who were just starting to get popular.
We hung out at the main stage and smoked weed allllll day, but looking at the wikipedia I realize I missed quite a few good bands on the side stages: Guided by Voices, The Verve, Flaming Lips, Pharcyde. Fucking good times... I am depressed now.