I like a lot of music, some Christian and some secular, not all of which necessarily fits the OP's parameters.
Listing all the artists would take a lot of time and thought. Here's a very abridged version:
Favorite secular genres: rock (all kinds, all periods, including metal and punk), jazz, blues, reggae, classical.
Some favorite secular artists, in no particular order: Christopher Tin (a modern classical composer), Cab Calloway, Leonard Cohen, Joan Jett, the White Stripes, Alison Krauss, Leo Kottke, Ry Cooder, Yo-yo Ma.