Can I use my regular 3.5mm headphones with a PS4?

For the PlayStation 4, you can just use a regular set of 3.5mm headphones to hear game audio through the port on the DualShock 4.

To do so, from the PS menu, go to Settings > Devices > Audio Devices > output to Headphones > With your headphones plugged in select "All Audio" as opposed to "Chat Audio." You can also adjust the volume from Audio Devices > Volume Control (Headphones).

I found the steps slightly different to the answer from @Teryx, maybe due to a later software update? This worked for system software 2.04:

First plug in your headphones to the DS4. Then:

Settings > Devices > Audio Devices > Output Device.

That should be set to "Headphones Connected to Controller".

As @Teryx said, on the same screen, > Output to Headphones should be set to "All Audio"