Code Geass and Angel Beats! were the main reasons that I still watch anime today. After that I proceeded with watching Toradora!, Durarara!!, Clannad, and many more. I've been hooked ever since. :D
The first one that I took interest in was Berserk around 2000. My cousin showed it to me and I was like "holy shit." Then I saw Cowboy Bebop on Adult Swim and that really got me hooked into anime.
I'd randomly download crappy .rmvb files from some download site of Naruto and Bleach and Love Hina but it wasn't until I got into torrenting that it really took off.
Now I use RSS feeds with nyaatorrents to download the latest seasonal shows automatically. Its nice to sit back and watch the downloads roll in. Time to install another 2TB drive...
The show that got me hooked into anime was Elfen Lied. I was moved by the story and ending and decided to give anime a try in hopes of finding something that would make me feel the same way as that first time I watched Elfen Lied. My second anime was Kannazuki no Miko, followed by either Neon Genesis Evangelion or The Melancholy of Haruhi Suzumiya. Not sure what came after that. Probably Lucky Star.
Mahou Sensei Negima. I know I had anime before this but I don't exactly know my first. It was with Negima back in 2005 that I learned of anime though and became engrossed in it.
I used to watch anime back when cartoon network aired toonami. But the first anime i really got in to was Rosario+Vampire. I got into it from a friend when he was reading the manga. I really liked it at the time and anime was still new to me. The story and the characters got my attention.