It depends on the band! I don't listen to Sonic Youth for their lyrics, I listen to them for the music (and the attending constellation of noise, feedback, and power drills being routed through distortion pedals).
I guess I divide the bands I like into two categories: Ones that make we want to play along, and ones that make me want to sing along.
Tom Waits makes me want to sing along. The music barely matters there, as he changes how it is arranged, and even which song to perform over which piece of music. I remember hearing a version of Eyeball Kid that was better than half Big in Japan (and the chorus was usually just him stomping around in a circle while wearing a mirrored bowler, that he switched back to the requisite pork pie hat for the verses). It was great. He also puts other songs in the middle of a song sometime, either in a concession to ADD or just to keep things fresh after all these years. Hell, sometimes he doesn't even use music until the end of a song. That breathing/beatboxing/subvocalization technique is enough to carry most of his boot stomp rhythm songs all by itself.
Danzig, at least up to a point, is a great guitar band. The pieces are technical, yet full of soul and dark vibes. However, who really cares when you have that powerful voice, almost equal parts Morrison, Elvis, and Orbison, howling straight through your soul? With Danzig, the lyrics aren't even as important as the voice that carries them. I put up with stuff from him (in more recent years, mind you) that would make me shut most other bands off - just because the delivery makes up for it (live, if not always on the album cut).
This duality has extended to my own songwriting. Some of my songs are all about the lyrics, the story or message I'm trying to convey. Others might have pure throwaway lyrics because the music itself expresses what I was feeling or tells the story I had in mind.
