The first Anime I ever watched was Naruto, since I'd heard about it on the Internet and saw it on Jetix one day. Watched a few episodes and found that it was repeating the same episode every day of the week >_>
Went to YouTube and watched the Eng Dubs up to Episode 81 and then Fansubs from then on. I watched every single episode, even the countless fillers and really boring episodes. I'm still following Naruto Shippuden, but, after watching other better shows, feel that it is just bad. I found Dattebayo's site and started watching Bleach. Every episode, again without missing fillers and boring ones, and I still follow it. I'm not sure why, because it's just not good any more.

Past that, I've watched:
Death Note, which I really enjoyed
FLCL. Oh. My. God. That was the best anime I have ever watched. I've never been so satisfied with another show.
Magical Shopping Arcade Abenobashi, which wasn't great, but was good to follow.
The Melancholy of Haruhi Suzumiya - but I think I watched the episodes in the wrong order. Was great fun anyway.
Clannad, which was almost identical to Haruhi Suzumiya, but slightly sadder.

I'm currently watching or following:
Code Geass - It's like Death Note with robots
Azumanga Daioh - But I've not really gotten interested yet.
Gundam 08th MS - I've yet to start
Evangelion - I've yet to finish downloading.
Hayate no Gotoku! - I got the first episode to see what it was like, and enjoyed it, so I'll get the rest later.
Fullmetal Alchemist - I've heard nothing but praise for this, so I'm hoping to enjoy it
Lucky Star - SCHOOLGIRLS AND DANCING.
Excel Saga - Also heard praise for this.
Elfen Lied - Violence and nudes :3