B737 FLT CREW RECEIVED A EGPWS 'TERRAIN' WARNING DURING VECTORS FOR APCH INTO LAS.

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WE WERE ON APCH CTL VECTORS TO A VISUAL FOR RWY 1R AT LAS; ASSIGNED HDG OF 280 DEGS AT 6000 FT MSL APPROX 13 MI SW OF LAS. TFC WAS FAIRLY HEAVY AND WE THOUGHT APCH CTL MIGHT BE BUSY AND FORGOT TO TURN US TOWARD ARPT. WE HAD TERRAIN MAPPING ON (I HAD 5 MI DISPLAYED AND FO HAD 10 MI) AND WERE VERY AWARE TERRAIN UP TO OUR ALT WAS CLOSING IN. FREQ WAS BUSY AND I ASKED FO TO ASK FOR A TURN; BUT COULDN'T WAIT FOR A RESPONSE FROM THE BUSY CTLR; SO I BEGAN A 30 DEG BANK TURN TO THE R; WHEN THE FO FINALLY GOT THROUGH TO THEM AND APCH CTL SAID TO TURN R TO 360 DEGS. I WAS ABOUT 1/2 WAY THROUGH THE TURN TO THAT HDG AND RECEIVED A 'TERRAIN' OR A 'TERRAIN PULL UP' WARNING FROM EGPWS. I STARTED A SMOOTH; BUT POSITIVE CLB. THE FO ADVISED APCH WE RECEIVED A WARNING AND WERE CLBING. APCH CTL TOLD US TO TURN TO 010 DEG HDG AND CLB TO 7000 FT; WHICH WE DID. A NEW CTLR CAME ON AND COMPLETED GIVING US CLRNC FOR A VISUAL APCH TO RWY 1R UNEVENTFULLY. I DISCUSSED THE EVENT WITH THE LAS VEGAS APCH CTL SUPVR AND SEVERAL EMPLOYEES AT MY COMPANY OVER THE NEXT 24 HRS. I BELIEVE TFC CONGESTION CONTRIBUTED TO THIS EVENT; AS WELL AS AN UNUSUAL APCH SIT (RWY 1R IS NOT A VERY FREQUENT APCH); AND HIGH TERRAIN IN ALL QUADRANTS FROM THE ARPT. IF WE HAD NOT BEEN MONITORING THE TERRAIN ON OUR MAPPING DISPLAYS; WE WOULD NOT HAVE BEEN AS SITUATIONALLY AWARE AS WE WERE AND MAY HAVE HAD TO DO A SEVERE BREAK AWAY MANEUVER TO MISS THE TERRAIN; IF WE COULD HAVE AT ALL. I HIGHLY RECOMMEND USE OF THE TERRAIN MAPPING MODE IN ALL NIGHT AND IMC CONDITIONS IF NOT AT ALL TIMES TO GET IN THE HABIT OF HAVING IT AVAILABLE WHEN YOU DON'T THINK ABOUT USING IT IN THE 'HEAT OF BATTLE' IF IT IS AVAILABLE. IF THERE ARE WX CONSIDERATIONS; 1 PLT STILL SHOULD USE TERRAIN AND THE OTHER WX; IF THE AIRPLANE IS SO EQUIPPED (LIKE THE B737-700 IS).