Do I have to take my clothes off?

No, it depends on the type of massage you are receiving. There are forms of massage, like Shiatsu or Lymphatic Drainage, where you are supposed to wear loose, comfortable clothing and no lubricant is used.

In a basic Swedish-style massage an oil or lubricant is used and it is customary to take off all of your clothes. If you are more comfortable leaving your underwear on, that's ok. When you leave on clothing you are indicating to the therapist not to work on that area. If you leave your underwear on it will limit access to hamstrings, glutes and quadriceps.

Note to the guys:
Boxer shorts cover almost one-third of the leg; if you wish to wear underwear briefs are better than boxers.