Country:

 Dolly Parton

Reba McEntire

Tim McGraw

Megan Moroney

Brad Paisley

Shania Twain

Rascal Flatts

Carrie Underwood

Rock:

There are muiltple subgenres I listen to, most of it is either Punk or New Wave so I'll seperate it between the two. 

New Wave:

Duran Duran

Ideal

Devo

Culture Club

Nina Hagen

The Specials

Thompson Twins

Nena

Punk Rock:

Ramones

Billy Idol

Other subgenres:

Motorhead