An air carrier Captain reported a near collision on the ramp in DEN.

Narrative

Near collision with [a] RJ--we landed on 16L and were informed that our gate was occupied. Ramp instructed us to taxi in and hold short of [our gate]. Abeam [the gate] I made a right turn to the green line when my First Officer yelled; 'Stop!'. I brought the jet to a stop and looked right to see [a RJ]. The RJ was taxiing at a high speed overtaking us from our blind side on the right. He never swerved nor appeared to slow at all. We came within 20-50 FT of the RJ. Ramp admonished the RJ and said that we had followed our taxi instructions correctly. If my First Officer had not 'cleared right' we might very well had collided! In over 40 years of flying this is the closest I have ever come to a ground incident. No passengers or crew were injured in the abrupt stop. We did not hear the RJ's taxi instructions so I don't know if he was warned of our taxi instructions. In my opinion the RJ was taxiing at an unsafe speed. While waiting for our gate we witnessed yet another RJ taxiing at a high rate. I would suggest that someone spend some time in Ramp Tower to observe taxi speeds. My takeaway from this is to expect the unexpected at all times and to once again thank my First Officer for his professionalism.