For me, it depends on whether I'm performing or just doing the engineering. If I'm just doing the engineering, I use whatever I have handy. The flatter the response, the better, since that makes problems like distortion or 60 Hz hum glaringly obvious, but honestly, I've never found a pair of headphones for over about $20 that didn't do a good enough job, so long as they cover the entire ear and don't just sit on top of it.... The most important thing there is isolation---being able to hear the mix sound without it being overwhelmed by live location sound.
When I'm performing, though, at least instrumentally---and I'm probably weird in this regard---I rather like noise cancelling headphones so that I'm able to better hear how my sound blends in the mix. It's the natural tendency of most performers to try to do so, and hearing only the mix means that I have to do less work riding levels later....
On the other hand, when I'm singing, I tend to work with one ear outside the can entirely, since that allows me better pitch perception (because there's less latency moving sound waves four inches around your face than through even the lowest latency software playthrough). In that case, again, whatever I have lying around works.
Bottom line, though, is that every person is different, and every environment is different, so pick a pair of headphones that you don't mind wearing for hours at a time. I think that's the most important quality. A pair of headphones that hurts... after a couple of hours in a recording session... like rope burns on your ears... not a pretty picture....