I got some bootleg DBZ tapes on a trip to NYC in '95. I had no idea who the hell anyone was (they all looked the same!), but hey, there was fighting and the subbers added in lots of swear words, so it was awesome.

Back then, I went nuts for:
-Anything Rumiko (Urusei Yatsura, Maison Ikkoku, Ranma 1/2, One Pound Gospel, Mermaid, Rumic World)
-Outlanders and Caravan Kidd (it's sad that Johji Manabe is a hentai artist these days)
-Fist Of The North Star
-Battle Angel Alita
-Riding Bean and later Gunsmith Cats
-Bubblegum Crisis
-The Dirty Pair (it's crazy to think that Adam Warren and Toren Smith did an American comic version in 1989!)
-The Sorcerer Hunters
-Ninja Scroll (It's the real Samurai Shodown movie!)
-Anything Masamune Shirow (Appleseed, Dominion Tank Police, Ghost In The Shell, although with the latter I found the movie version incredibly boring)
-The Street Fighter II anime movie
-And of course, Akira. Akira was the first time I remember a Japanese cartoon being advertised for being "mature" and not localized for the kiddies/western audiences. Everyone remembers "Leonardo" as Kaneda. The Streamline dub is still my favorite version of the movie, just because it was burned into my brain as a wee third grader.
Ranma was easily the biggest thing back then. It was the most-popular manga and anime by far. You had the comics, tapes, calenders, posters, and t-shirts. I had them all.

And yet its popularity pales in comparison to the likes of Sailor Moon and Dragonball, which would come over here later.