Well, the lead-up to me really getting into anime was a slow, slow burn of Tenchi Muyo, Sailor Moon, DBZ, the odd Naruto episode, and some other assorted things - it's always been a part of my greater entertainment experience. And then, of course, I binged all of Ouran and that was a true experience, let me tell you.
I would have to say that the thing that tipped the scales, though, was probably Code Geass. It had just the right amount of mechs, mysterious candy-colored-haired semi-goddess women, Pizza Hut product placement, and pseudo-psychology in it that it became one of my favorite series, and remains so to this day. But all it really did was inspire me to get off my butt and watch all of Evangelion, and that's the one that really hooked me, since it actually demonstrates the artistic efforts of its creator and in general is just pretty amazingly well-done. Plus, it doesn't hurt that there's vaguely implied symbolic gay romance for like one scene!
So yeah, Eva, I guess. Now I spend my days literally agonizing over the fate of a pink haired oni girl in a blatant, um, spiritual successor to Eva - everything really does come full circle.