Do standard headphones work with the XBox 360 controller?

You can use standard headphones to listen to game sound, but not by connecting them to the controller. You would need to use a television with a headphone jack, and then jack into that.

Some fancier headphones will come with an optical hookup, which can be connected to back of the Xbox itself. I have a Turtle Beach gaming headset. It connects to the controller for the voice communications, and the Xbox for the game audio.

No. The xbox 360 controller has a 2.5mm jack but it is used for voice communications only, no game audio. Headsets that carry both game and voice audio require you to plug directly into the TV or the xbox to get the game audio.