I just found a glitch I thought was funny. I don't know if I'm the first, but you can go through the game headless.

To do this you need an Archmage's Robes. You get this robe after finishing "The Eye of Maguns" quest.

The other item you need is the Morokei Mask (you get this after defeating Morokei. He is found at the end of The College of Winterhold quest line).

If you put the Robes and the Mask together, then your head won't be there until you change body armor.

PS: You can still have light or heavy armor for your hands and feet.