Oh, that was easy! (I wonder why I have a mental block about these things... it's not a direct 'save as' link, though - you do have to click through to the site briefly if you're desperate to hear some of my awesome teenage taste.)
I forgot to say earlier: Lawrence specified songs you liked at the time, not songs you discovered years later. This makes everyone's list a little less cool and a little more truthful! So I might as well be chronological and start with 1990, a year lost so far in the mists of time that even my horrible perm is now invisible... thank god. I was fifteen.
Dub Be Good To Me - Beats International
You have to hand it to Norman Cook here: it's an early sort-of mashup! The Clash with the SOS Band, I believe. Of course, this is with the benefit of a 'series of tubes' and years of music-nerd-dom behind me. At the time I had no idea what made up the constituent parts, and I just thought that this was, erm, 'jam hot'. Luckily, I still do. I've heard this song 20 times over the last few days and I completely love it. So what does 'Tank fly boss walk jam nitty gritty' mean anyway? And what's up with the awesome humming-dude breakdown? How on earth did anyone think of doing that?