I watched DBZ, Pokemon, Yu-gi-oh, and Naruto pretty religiously as a kid. Though I wouldn't say those were what got me into anime.. since i didn't even know what it was at the time!
The first series I watched that really got me wanting to explore anime was soul eater!
I started with Pokémon, Yu-Gi-OH and Monster Ranchers as a little kid and then found more anime on Toonami and Adult Swim, that's how I first started watching anime.
I was flipping through the channels and saw some anime with fighting and power magic I thought at the time. it looked to me like some Chinese anime because I saw the symbol in the bottom right, but it was just DBZ kai goku vs vegeta as a giant ape xD then I got hooked onto all the good anime....
Watched a bit of previously mentioned ones here like dragon ball z or pokemon but not much. Think it began when Travis recommended Sword Art Online. Then I watched a bit of Attack on Titan. Haven't really given others much of a chance or time.
My first title was SAO just after it came out :smile: Got recommended by a friend, and really got into it. However, watched Shaman King before, while it was on the TV, lol.
Anime got me with it's epicness, variety of topics and relatability to characters
First anime was dragon ball z on cartoon network and then followed shortly thereafter by naruto. I got really impatient waiting every week for new episodes to come out so I watched naruto online on a "watchanimenow" kind of website, and the rest after that is history.