I used to listen to J-pop a lot when I was younger, and I think moreso because the bands were Japanese and I liked the bubblegum sound of it all. I've since thrown away my burned CDs of most of that stuff because I'll be honest, I'm really not an Utada fan.
But there's some Japanese music that I really love - again, it's not necessarily the song lyrics or meaning (in some cases it may be) but the overall sound. Fantastic Plastic Machine, Pizzicato Five, Cibo Matto (NY band actually, but Japanese ethnicity). They get lumped into a category 'shibuya-kei' so I do try to seek out other Japanese artists because it's a Japanese music genre, but it's influenced by bossa nova, jazz, pop.
There's also a couple of Japanese rock bands that I like. One of my favorite bands is GO!GO!7188 and I like a lot of their older stuff which I would generalize as surf rock. But I also listen to The Ventures which are a similar genre.
Hm, but I'm a bit out of the norm. As Nick puts it, I listen to "weird stuff".