There are waaaaayyyyy too many to list, but since you wanted to try out some bands, here's a few that spring to mind right now. I haven't listened to Chinese music for a pretty long time though.

(You probably know who they all are, but just in case you don't... I put some extra info)
Nicholas Tse: I love this guy. <3
Machi: You should really give these guys a try. They're Taiwanese, but the members grew up in LA and they mainly sing hiphop.
Eason Chan: He's good. That's all I can say that isn't totally weird and irrelevant.
Alan Luo: I don't like him, but his music is pretty addictive at times.
Alan Kuo: He did the themesongs for Mars (Ling) and Say Yes Enterprise (Pin Le). Both more rockier-type songs. I love most of his songs.
Lin Jun Jie/JJ Lin: A Singaporean singer. "Jiang Nan" is his most popular song.
Soler: More of a rock-ish type of band from HK. But they're like mixed Italian or something @_@
Twins: I'm not a fan, but they're very popular.
Boyz: They're like a male version of Twins lol.
Kenny Kwan: Ex-Boyz member gone solo.
183 Club: Made oh-so-popular by the Prince Turns To Frog series. Typical pop to me.
Mayday: I don't listen to their music, but I've witnessed their popularity. x_X
Leon Lai: One of the four kings. He looks like he's kinda plastic now though @_@
Aaron Kwok: One of the four kings who can dance. XD
Leslie Cheung: Oldies.
Alan Tam: Oldies.
Miriam Yeung: She used to be considered Sammi #2, but she's definitely made her own now.
5566: Part of the boyband wave. I don't even know if they're still as popular as they used to be.
Guang Liang: My friends always sing "Tong Hua" at karaoke, even though the MV is totally retarded.
Justin Lo: Apparently his voice is good.
Kevin Cheng: lol he sings now. No idea how he sounds!
Wallace Huo: I really liked his album, even though it's old now. Ballads, mainly.
Angela Zhang: A song that was played constantly whilst I was in Taiwan was "Pandora".
Fish Leong: Almost everyone loves "Yong Qi"
Hacken Lee: He's got a great voice.
Leo Ku
Penny Dai: Umm... try, "Ni Yao De Ai"
FIR: I really liked "Lydia".
Huang Yi Da
Vivian Hsu
Bobo Chan
Energy
Candy Lo
Jeff Chang
Stephanie Sun
Zayin: The members grew up in Australia. Think their songs are old now though

;;