I guess the anime to really get me into anime was FLCL
My mom had just gotten Netflix for the family to use back when I was in Jr. High because we thought cable was pointless. We got it, and what I got in return was a whole bunch of anime to watch.
The thing is, the only anime I had ever seen was stuff on Toonami. Stuff like Naruto, Bobobo-Bo Bo-BoBo, One Piece, Zatch Bell, and more. But by the time we got Netflix, Toonami was in the void for a long time. So I guess you could say my anime watching experience was quite limited when I was a kid. (And yes, I am a lot younger than the majority of people on this site. I didn't get Bebop, Trigun, or Outlaw Star when I was a kid.)
So anyway, when we got Netflix, I was astounded by how much anime there was on there. And there was even gory stuff that seemed almost forbidden to watch at the time. I browsed through the collection of anime until I found a cover that really stuck out to me. Huh. A girl playing a guitar with a nice array of varied colors in the background. And it says it's only six episodes. What I didn't know about the show was just how fucking crazy it was going to be to watch.
I watched through the whole thing in one sitting and was blown away to say the least. The music, animation, and finale all combined to make a marvelous package of something I had never experienced before in my life. It was crazy, stupid, and fun. That's when I decided that FLCL was going to be my standard for quality anime for years to come. And it still is.
I own the show now, and watch it constantly.
As an artist, it's inspiration.
As a viewer, it's stupidly fun.
It's pretty much my favorite anime and it's the show that got me into watching anime.