The first anime I watched was Fullmetal Alchemist.
Though technically, I had seen some episodes of Dragon Ball Z and read the first volume of the One Piece manga.
From FMA, I went on to read the FMA manga up to the point it had reached, then watch about 40 episodes of D.Gray-man. Over the next years I would occasionally watch some episodes of some anime such as Evangelion, Hellsing, .hack//Sign, Cowboy Bebop, Trigun, and Fate/Stay Night. I would not stick with them.
It was not for some time that I actually started watching whole series of anime again (I had, however, been reading D.Gray-man and Fullmetal Alchemist).
Time here gets very fuzzy.
I probably started when I heard Fullmetal Alchemist: Brotherhood was going to come out. Somewhere between then and when it reached ~episode 35 online in official subs, I began following its progress and stopped buying the manga, I watched Soul Eater, I watched about 80 episodes of Bleach, and I watched the entirety of D.Gray-man.
Time here stops being fuzzy.
One day I watched Gurren Lagann with my brother. I suppose you could say that is what really got me started on anime, in the sense that after that I really began watching series from start to finish rather than the sense that "I like anime". Almost a year after that (early this year) I watched Trigun, then Cowboy Bebop, then Code Geass, then Hetalia, then Wolf's Rain.