Totally depends on the kind of music!
If you're talking RAWK ( guitars, vocals, bass, drums ) then I'd try and get the drums balanced internally / relatively first, then sit the vocal over. Probably bass next, then the rest. I suppose it's a "top down" approach - loudest first!
For more abstract stuff, which is much more my bag, it's really an integrated exercise. I'm mixing all the time as I lay tracks down or take tracks away - the mixing can have an impact on the song and its structure and vice versa. The idea of "mixing" as a distinct phase of producing a track really doesn't apply.
For example, the quick track in the previous thread - I never got to a point where I thought "right that's all the parts down, lets try and mix them".
However, I guess what's common to both approaches is sonically I'm always trying to achieve separation between parts - making sure each one can be heard balanced within in its own frequency range and point in the stereo picture, so that each contributes to the song!
BS