I think for a lot of us growing up in the past 30 years, the appeal of Japanese media has been that it's always been willing to break the barriers that our domestic entertainment typically doesn't. The animation medium isn't viewed as solely for kids over there, so you tend to have a much wider variety of available shows for different audiences. When you become a teenager, you start to want some "cooler" shows to watch, and if you want an animated show that isn't a comedy, where else are you going to go?
That doesn't make you an "otaku", though it might be the beginnings for a lot of people. I think you only get called one if you enjoy some of the seedier things they produce that a company from any other nation would never make. Got Senran Kagura video games, Queen's Blade on bluray, Monster Musume manga, or own a cast-off figure or two? I'm guilty of all of that, but I wouldn't think of myself as an otaku. There's plenty about those things that embarrass even me, but there's also kind of a liberating, guilt-inducing, carefree pleasure to them. It's like if you intentionally choose a movie that's rated R instead of PG-13.
I love Ghostbusters, Indiana Jones, Tron, and the Simpsons, but I also happen to enjoy Ranma 1/2, Lupin the 3rd, and old Toshiro Mifune samurai movies.
