For J-pop: There's Utada Hikaru (You may know her from Kingdom Hearts), she's really good. I like her voice--she's one of the best yet, if not THE best.
Crystal Kay is good as well. And I'm sure if you like her, you'll LOVE Koda Kumi. (Mmmm....)
J-rock: I'm a huge fan of Dir en Grey. I like their heavy riffs and their metal screeches! One of the best bands out so far. Also, The Pillows (known for their work on FLCL) is one of my favorite bands ever! I love their indie style songs and their random lyrics.
J-rap: The best j-rap group right now is Rhymester. With their solid beats, astonishing lyrics and rhythms, you can't get any better than that. In a close second is Rip Slyme. I'm a fan of drum n' bass, so when I heard there's a group that raps over it, I was like, "SWEET!!" Then there's the ever popular Kick the Can Crew! Discovered by Rhymester, these guys are great! I love how the three interact with each other in their songs and their music videos. They're a pretty good group.
I hope I helped a bit. There's tons more, but I don't wanna get in trouble for turning this in to a list thread. >_<