A B737NG Captain reported an airborne conflict that resulted in a TCAS RA and the advantage that TCAS offers. He also stressed the need for traffic vigilance below 10;000 FT.

Narrative

After take-off on Runway 10 we were assigned runway heading to climb and maintain 8000 FT. Tower handed us off to Chicago Center. Approaching 8000 FT we were cleared for a higher altitude. Then we received a TA alert and at the same time ATC notified us of traffic at one thirty; all of this happened simultaneously and both the First Officer and I visually saw the other aircraft then we received an RA; 'Descend Now; Descend Now'. At that moment; I simultaneously manually pulled the power back to flight idle and pushed the nose over and turned to the right while descending and maintaining visual contract with the intruding small aircraft. As to how close we were is unknown. I can tell you that it was a Cessna RG white with red and black trim. I could also see the N-numbers and the two pilots. ATC was not talking to the intruding small aircraft and that Aircraft was operating under VFR Rule. Vigilance when operating less than 10000 FT in VFR conditions is a must. Automation and so called 'Smart Aircraft' like our 737NG aircraft are a great asset to us and to the safety of Flight Crew and passengers. We as pilots have to remember that there are other pilots and small aircraft that still fly under VFR rules and they also have a right to use the airspace all so. Our 737NG aircraft are TCAS equipped and it's a great tool. We also have a window to look out of also. In this RA event; I used the automation and in addition was able to hand fly the aircraft while maintaining visual contact and a safe distance thus avoiding the intruding small aircraft.