The Anime that I didn't know was an Anime, Digimon, when I found out about that, I decided "Huh, its not all just tentacle sex and demons raiping people..."
THEN I found out that my favorite video tape series my mom got me as a kid was an Anime.
Sherlock Hound.
That proved to me that anime was awesome, and I think it cemented my love of Steampunk that I have now.
For me, it's probably The Melancholy of Haruhi Suzumiya -- it was hella lot of fun. Plus, it was the first anime I streamed xD
The ending sequence dance was pure win, plus the plot about the girl being God, a Time-fault, and the key to auto-evolution was rather unique and enjoyable. I liked the anachronistic order as well. Basically, it was waaaay different from the typical hack-and-slash, straightforward animes I liked to watch in the past. It kinda opened new windows of opportunities for me -- that anime can be quite diverse. I'm open-minded right now with anime because of Haruhi :p
Plus points to Rozen Maiden, being the first anime I downloaded. Creepy kawaii dolls + battle + moe moe moe overload hahahah demmit....*nosebleed*
While not techinically my first, Zoids: Chaotic Century is what started me down a path of being addicted to anime. Even though I spent a few years afterwards without regularly watching anime, it was definitely the catalyst in the whole situation.
Like many, I saw numerous things before I knew they were actually from Japan; Vampire Hunter D, Dragon Ball Z, Bishoujo Senshi Sailor Moon, Beast King Go Lion (aka Voltron) and a few others. However, the real kicker for me was reading about it in a gaming magazine and it dawned on me... oohhhh this is what that is, now I get it. Then came Gundam (still my first love) and a list that's too big for me to want to post on MAL. I began my fandom in 1996 at 13, been hopelessly addicted ever since.
Probably the one that 'changed' me the most was Evangelion.
Watching the entire series, marathon style, twice in a row at 14 was SO not good for my mind. Felt kind of depressed afterwards...
Me... It was Clannad, heck, when I finished watching the second season, I started to be more aware of my entourage and I started to be more sensible... Clannad also proved to me that I can still cry. After watching the anime, I also became a lot more kind to the people in my surroundings...
Pokemon, first exposure to anime. Got me hooked. Digimon got me coming back everytime cause it was so awesome especially when Greymon evolved into MetalGreymon to fight Piedmon.
I did GameZource. And believe me, im a great fan of Key.
I just think that, Tomoyo After, the direct continuation of tomoyo end, is betterrr... it just pisses me off poeple forget about Tomoyo (T_T
Like every other little kid, I watched DBZ on tv when I was a kid. But Spirited Away just blew me away. It was unlike anything else I've ever seen. The pure imagination that went into that movie was incredible. Made me absolutely fall in love with not just anime, but Japanese culture.