This is going to be a mix of Korean and Japanese pop, bear that in mind, before any one yells at me for mixing up ethnicities.

Namie Amuro (<3)
Morning Masume (giant girls group that switches line-up every few years)
Ami Suzuki (FREE FREE is one of my favorite songs of ALL TIME)
Kumi Koda
Utada Hikaru (also look up her English stuff under the name Utada, love her!)
Girls Generation (Youtube "Gee" - cutest song EVER! They're kind of like the Korean Morning Masume)
Ayumi Hamasaki
Super Junior (Korean boys group)
Big Bang (Another really awesome Korean boys group)
Crystal Kay (half black - half korean singer who was raised in Japan)

Those are the obvious ones that come to mind. There's are a lot of people out there.

EDIT: I dunno if you're interesting in J-rap but Teriyaki Boyz are like, seriously one of my favorite groups out there. They're really fun and have a lot of collaborations with famous hip-hop artists.