Well, I'm busting on Rush pretty hard, so I guess it's only fair that I lay open my musical tastes as well, unsolicited:
The Rolling Stones, The Who, The Allman Brothers Band, [early] Springsteen, King (B.B. and Albert), Stevie Ray Vaughan, Eric Clapton, J. Geils Band (blues and pop), Big Mama Thornton, Elvis Presley, etc.
But, since you asked, I'll say The Beatles, Tom Waits, Leonard Cohen, Marah, Robert Earl Keen, Junior Brown, Flaming Lips, Elvis (both of them), Emmylou Harris, Richard Thompson, Fela Kuti, The Saw Doctors, Son House, Dwight Yoakam, Richard Shindell, Maceo Parker, Greg Brown, The Pogues, Van Morrison, Dramarama, Everclear, They Might Be Giants, Willie Nelson, Habib Koite, The Temptations, Marvin Gaye, Israel Kamakawiwo'ole, Sargent Garcia, The Four Tops, Taj Mahal, John Hiatt, Nine Inch Nails, Holly Cole, Joe Jackson, Stan Getz...
I'm sure any Rush fan can make fun of at least somebody on that list, but I won't agree with them, and I'm always right. 8-)