As a child of the 90s, I can think of a lot of influences, though no direct icons fashion-wise. Kathleen Hanna and the whole Riot Grrrl scene. Ani DiFranco and Sinead O'Connor. Courtney Love. I have a real soft spot for the 90s, and how 70s/80s punk/new wave/no wave styles evolved into grunge and its variants. Oh gosh, not to mention ska. Those ska kids rocked some amazing looks.
I think the angry/rebel girl really came into her own in the 90s. Third-wave feminism came at style and sexuality from a very different angle than second-wave feminism (from the bra-burning 60s to the power suits of the 80s, all of which I have a hard time identifying with on a personal level, though I get it historically), and that's left a pretty lasting mark on me, more than any one person.
RoseandJoan, I've always loved Winona Ryder's style, too.
Viva -- your associations with Carolyn Bessette are exactly what come to mind for me too (half of my family is from Greenwich CT). Beautiful, effortless, and oozing privilege -- it's that very particular sort of Long Island aristocratic look, and she did execute it very well.