I'd say my first was Gundam Wing. Then things like Trigun, Cowboy Bebop, FLCL, and various Shounen series. From there I learned about subbed Anime and never turned back.
Unless you count DBZ and Pokemon in childhood, it would have to be Claymore. Man that hit me hard, having never really watched any dark fantasy stuff I found Claymore brutal, still love it though.
First anime was probably Dragonball from Toonami when I was a kid. Back then I thought it was all just cartoons. What really got me into anime was probably Fullmetal Alchemist - I started watching Brotherhood on Youtube when it was having its TV shows / movies phase.