PlayStation VR users have discovered that you can play Xbox One and Wii U games while using the headset.
Plugging in either of the devices to the PSVR's processing unit will display the console's output in PSVR's cinematic mode. This mode displays the console's output on a big cinema screen in front of you, however it often isn't ideal due to the headsets relatively low resolution.
Another reported issue is to do with the sound. Neither of the consoles seem to work with the 360 degree audio that PlayStation VR uses and as a result sound is not naturally made by the PSVR. Plugging a headset into the console or finding another way to broadcast the audio away from PSVR does seem to work.
Some people have reported that it is also possible to use a PC with PSVR, others however have said that the device does not recognise the input.
While it is nice to have a cinema sized screen in front of you to play games on, those with a big TV would probably be better off just using that. The low resolution of the headset and the lack of sound means that while it is cool to use, it probably isn't the best way to play your Xbox One games.