I think I listen to music differently to most of my peers. How I listen to a particular song is somewhat genre-specific, but mostly it'll be the music that catches my ear first. I'll listen to every single element that makes up the song, identifying the ones that I like and the ones I'd change, how it connects with the rhythm and the melody, whether it fits in with the message the lyrics are trying to send out etc. Maybe I'm over-listening.
I mainly listen to House of the soulful, jazzy, deep and funky varieties. When it comes to House music, it's all about the music. The lyrics are a distant 2nd, probably because alot of the songs don't contain any lyrics at all.
For rap, it's more the beat/percussion. All my favourite rap tunes have this quality that just makes me act all gangsta.
Like Tophat said, when the lyrics become part of the percussion, I give an extra big-up to the artist. Notorious B.I.G was a great example of an artist who was all about the rhythm and the rhyme.
My rock listening is lyrics-driven, with a good quality musical performance (I prefer real instruments to synth sounds in ALL genres) to back it up.
I don't care who sings what. I listen to every song on it's merit and decide whether it's good or not. Put 6 or 7 good songs on your album and I'll most likely buy it, but I try not to let past greatness influence my decision.