Must-haves:
-noise cancelling. Cover the entire ear and enclosed (some that cover your ear are open to the air and thus not noise cancelling)
-wired. I don't want to deal with batteries.
-inline volume control. My cheap pair had it with a little wheel on the wire and I can never do without it again.
They also obviously need to have the small 3.5mm plug.
I have onboard realtec ALC892 sound which is good but not quite as good as my old audigy 4. It's still realtek's best offering though, at the time, so a decent pair of headphones will be useful. That basically means I don't need an audiophile's $300 pair of headphones, but I don't want a cheap $50 pair either that will sound average at best. I guess the $100-$150 range is okay.
I trust your opinions on this site, and there's simply too many headphone choices out there for me to choose without getting informed opinions first.