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I liked Dragonball Z as a kid and young teenager, but I really didn't think of it as an "anime"; neither did Speed Racer and Pokemon, which I watched sporadically, strike me as being un-american shows. I knew they came from Japan, but they were dubs so it felt like a normal cartoon. Everyone in the entire freaking school watched DBZ, but only the nerds watched other animes. So it really didn't count in that sense.
For me, the gateway anime was Naruto. It came to the US as the dub in late 2005, and I had no interest whatsoever. The previews showed this annoying brat who was supposed to be a ninja and said "believe it" way too much. WTF? By chance, I happened upon the first episode at a reshowing near midnight, and of course that changed my mind completely. I felt a connection with Naruto and his isolation and loneliness, something I had not really experienced with other characters in other shows. I watched it for several months, and then the big shift happened when I began to get IMPATIENT. I remember specifically: it was in the middle of the Rock Lee vs. Gaara fight at the Chuunin Exams, and I wanted to see the end of it. But the next episode wouldn't come until next week. But I wanted it NOW! So I went on youtube and was surprised to find someone had uploaded the entire freaking series so far (at the time in the midst of filler-hell, so the entire Part 1). I'd watched subbed stuff before so that was no problem. It was addicting, though. I was on break between college semesters with a speedy internet connection for the first time, and I'd watch about 10 episodes per day.
Around that time, I started to watch dubs of other animes showing at the time. Inuyasha, FullMetal Alchemist, Neon Genesis Evangelion; and because the internet was a thing, subs of several more. It didn't wake me very long to figure out that I liked the subbed version better, so it's gotten to the point where I watch them all the time.
The gateway manga for me was HunterxHunter. The reason was very similar, actually. I started watching the anime (subbed of course, there was no dub yet) in late 2006 and early 2007. It did not take long for me to finish it, but then I was told by a friend that the story continued PAST the Greed Island Arc where the anime and series of OVAs had ended. So, one night, bored, I pulled up the manga and started going at it. I think I probably got all the way through the greater part of the Chimera Ant Arc up to the point where there was one of those cursed hiatuses, in only a few days.
I don't read very many mangas, though. I read it and the new chapters of Naruto; and while FullMetal Alchemist was still going I got into that, also, right around when the Brotherhood anime started. I was (I'm so predictable...) bored one day and decided to look at what the latest chapter was. It was where Pride had filled Al's armor with his shadows and was about to fight with Ed. I remember thinking: "Is- Is that freaking Selim?? WHAT?!" because of course up until then I only knew him as the useless little kid from the first anime who was strangled by Bradley. I just HAD to find out what happened next, then.