The first I watched and enjoyed?
IRIA: Zerum The Animation.
Prior to this I thought all anime was trash. After this I began eating it up ravenously. I saw it on the sci-fi channel late one night. I was jogging and it came on and the opening hooked me, with the team trying to pull a search and rescue on a ship that happened to have a monster on it.
At the time the toonami line-up and adult swim were just getting rolling. Before Adult Swim there was the Midnight Run. Soon I was swimming in Outlaw Star, Gundam Wing, Cowboy Bebop. Good times. Rented Record of Lodoss war, loved it. I picked the first disk of Berserk up at best buy, was only 14 bucks. I wound up buying all of them the day they came out.
Sci-fi channel was showing anime at the time late nights sometimes before catoon network got going. I got treated to Armitage the third, Ghost in the shell, Akira and Vampire Hunter D that way. This was a very good education in anime and a very fast one. To this day when the girl shouts at the end "I love you Iria!" I can't help but tear up a little. Takes me back a long way. Thanks, Iria. It's good for a person to find out when they're a fool. You showed me that.
Eventually I got ahead of the curve. Heard about FLCL from newtype, bought it before it came on cartoon network, was dling fansubs of bleach and claymore years before they came out here. Bought Memories on the author's rep alone. Bought Hellsing after a friend recommended disk one. Then I just stopped. I guess mostly the good stuff dried up, or I'd absorbed my limit. Every now and then I'll see a show I enjoy like GunXSword, Full Metal Alchemist or Cromartie High but the barrage we saw in the early 2000's hasn't been matched and I've come to learn a lot of what's produced is utter crap,(like in anything else) but I've learned there's some gems in the pile and I've still been left with a positive view on the medium.