I think it's hard to find people in pop music (be it pop/rock, pop/country or pop/r&b) who don't do some screaming. However, they run rampant in other genres. I listen to a lot of musical theatr and right off the top of my head I think of Judy Kuhn, Marrin Mazzie, Kristen Chenowith and Lea Salonga.
I have to disagree with some of the suggestions. Ann Wilson, Pat Benatar, Chaka Kahn and Idina Menzel are all pretty much known for screaming (I happen to be a HUGE fan of the female scream-sing, so some of these are my favorite singers). I don't think it has to do so much with control as it is a choice. Ann Wilson doesn't scream because she has to, she does because her idol is Robert Plant and that is the style she is going for. When she was hired to sing Almost Paradise for the Footloose soundtrack, the screaming didn't fit the song, so she didn't scream it. Joan Jett is another great example of someone who alters her voice to the style of the music, but insead of a high belt scream, she puts the rough edge in her low notes.
I like Amy Lee, but sometimes she sounds like she wants to scream, but just can't quite get there.
Barbra Striesand used to be a screamer (come on---listen to the end of "Don't Rain on my Parade), but like Bette Midler (who used to be a MAJOR screamer) has calmed down. Little Barbra (Linda Eder) isn't really a screamer, but like Amy Lee she sometimes seems to fall just short of the emotion she's trying to get.
I think Sarah Brightman is a good example of a non-screamer. Even on her more poppy stuff--like the album Fly--she stays away from the full-out scream, even if she does get a little shriekey. But, part of this might come from her training. Even though she started as a pop/disco singer, she's always been fond of classical music. Her hybrid of pop and classical doesn't really lend itself to screaming.
For some reason I really just can not stand Carrie Underwood's voice. I don't know what it is. I recognize she has talent, but I just don't enjoy listening to her sing
