Well, I was born in 1993. It doesn't look like I've seen any anime that came out that year (though Sailor Moon is close), but one I found was "The Irresponsible Captain Tylor." It's a 26 episode humorous space opera about an easy-going crewman who is given command of a space cruiser in the midst of a space war. So I'll have to check this out because it certainly looks interesting!
Also tagging @NikolasSatterwh