A320 flight crew braked at the last second to avoid an encounter with a fast taxiing B737. May have missed a call by ground control.

Narrative

The flight was uneventful until after landing in Denver. We landed on runway 16L; exited on taxiway F4; and turned southbound on taxiway F. The First Officer checked in with the ground controller; who instructed us to taxi to our ramp via taxiways F and CS. I then instructed the First Officer to check in with the ramp controller. He did so; confirmed our gate assignment; and then returned to monitor the ground control frequency. As; we approached CS; the First Officer switched back over to the ramp frequency to get clearance into the ramp. I also started to monitor this frequency while still listening to the ground frequency. Both frequencies had many radio calls occurring at this time. As I started my turn onto CS; the First Officer turned to me to tell me that we were cleared into the ramp. He then called out for me to stop. I looked over my left shoulder; and saw a B737 taxiing south on taxiway G at a relatively high rate of speed. I abruptly applied the brakes; and brought our aircraft to a stop. The 737 proceeded through the intersection toward runway 25; with no apparent reaction to my aircraft. I called the flight attendants; and confirmed that no one was injured; and then proceeded uneventfully to our gate. After the 737 passed us; and when the First Officer could talk to the ground controller; he queried the ground controller about who had the right of way. The controller said something to the effect that it was his fault; but that he had called us; however; we failed to respond to the call. After we blocked in; I called the tower supervisor; and spoke to him about the incident. He tended to respond that we missed the radio call; which I did not hear. I don't know if the call was blocked; or if we just missed the call with the numerous radio calls which were occurring at the time we were taxiing onto CS. I should have listened closer to the radio calls; and kept a better watch on the traffic around us. I did clear to my left as I was approaching CS; but I did not see the 737 as a threat since I thought he was too far away to be a conflict. I must not have perceived his rapid taxi speed. The First Officer did a great job in alerting me to the threat.