The other night I had a bit of trouble finding a definitive answer to this question, so I figured I’d answer it for anyone else wondering the same. Yes, just about any set of headphones will work with the Xbox One headset adapter (for game / chat sound at least).
Since I’m ‘deployed’ and have a roommate I had been previously plugging my Bose headphones into the TV so that I could game without bothering anyone, however being able to plug my headphones directly into the controller (via the adapter) has made things much more convenient. You can receive game and chat audio wirelessly via the controller, though not all headsets will work for chat (it would seem inline microphones won’t work).
Gumballs Plays Games 
so if i just but the xbox one stereo heaset adapter and plug in my Sennheiser HD 205 II i would be able to hear game audio fine ??
Yup.
so, regular headphones won’t work to talk in game?
Just any headset with a microphone? I don’t believe so. Some gaming headsets may be compatible with the adapter or the new controller, but I can say what with my Apple earbuds and my Bose headset they only work for audio via the adapter.
I actually discovered that if the headphones are CTIA standard they will work with the adapter for in game chat, but headset Brands like Bose and the Apple EarPods aren’t compatible because they are MFi (Made for iPhone) and the pin arrangement is different from most headphones. To counter this you need to buy an adapter that switches the pins.
thanx for your reply earlier, i bought the controllers adapter and both my sennhieser headphone and my samsung and iphone earphones are working fine with the adapter also the samsung and iphone ear phones with mic also allow me to chat.
How did you get your iPhone headphones to work?
I just plugged them in. They work for audio but not the microphone