Vampire Hunter D Bloodlust got the ball rolling for me. Saw it on the shelf and the artwork and premise looked interesting. Loved it!
After that, I asked the guy at the video store for recommendations and ended up binging Evangelion next. Then I was a goner and just started devouring what the clerk suggested and rarely found anything from his list that I didn't love.
By the time I caught up on all the classics, a ton of absolute classics came out around the same time, and I wondered if there were actually any bad anime. :P
All within a year or 2 was:
Gurren Lagann
The Garden of Sinners
Sword of the Stranger
Moribito: Guardian of the Spirit
Kanon
The Melancholy of Haruhi Suzumiya
Utawarerumono
I'm sure I'm forgetting some, but I wondered at the time if it would always be this good. Feels like a bit of a golden age now.