In Army Basic Training we actually got some instructions on how to pack! We were told to fold our shirts in thirds lengthwise, then roll them up from the bottom with the buttons facing out. It worked fine for fatigues but it never works for my dress shirts.

If you have your shirts washed at a dry cleaners, ask them to box instead of hang them. I'm not sure if many cleaners still do that, but it sure makes them easier to pack.