This depends on the type of massage and the depth of the strokes. A light, relaxing massage that doesn't probe very deep into the muscles, shouldn't hurt. With that being said, there is a 'feels good' hurt and an 'ouch, stop it' hurt. A good massage, even a really deep tissue massage, should always stay in the 'feels good' hurt range.
Pain can be an indication that the muscle is possibly injured or inflamed and pressure should be adjusted. Also, pain can cause you to tighten up and negate the relaxing effects of the massage. The most effective and deepest massage always works with your body's natural response, not against it.