Everyone else has their "the first time I heard them" story, occasioned by the sad death by cancer of Adam Yauch, so I'll tell mine.
I was in grade 8, an alienated geeky kid who liked the anger in "Fight For Your Right To Party" and understood it to be more political and punk than self-indulgent. Rap and hip-hop didn't exist in my little part of Alberta, not until Run-DMC hooked up with Aerosmith - in fact I think there might have been one black family in my entire little city of 60,000. I think I was discussing the lyrics with my best friend, similarly alienated and geeky, when one of the cool kids who also considered himself smart enough to guard taste sneered out something about juvenile and spoiled brats. (The same guy thought Bob and Doug Mackenzie were juvenile and spoiled brats, and hey, those guys never went anywhere.) So I pretty much didn't listen to them again until grad school. There just wasn't anyone around who might also listen to them, and besides grunge was finally melting through the firewall created by Eagles cover bands and their cancon equivalents.