This is certainly a debated and controversial topic. You can find opinions all over the place. For one insight, see:

http://www.fitwerx.com/NewFiles/Bicy...esistance.html

Explanation and Tech talk:

Rolling resistance is the amount of energy required to overcome the friction between the road and tire. It sounds simple, but what effects it and how it works defies common thought. The key to understanding rolling resistance is to understand that it is determined less by size of tire contact patch than consistency of tire contact patch and that many variables from the vehicle’s tire pressure, tire width and tire construction, to its weight, to its frame design and how it effects sprung vs. unsprung weight all play a part.

We’ll discuss each variable individually, from less complicated to more. Just keep in mind that the real thing to understand from all this is that consistency, not current, tire contact patch is what really counts in minimizing rolling resistance. The methods of how to keep the tire contact patch consistent is where it can become difficult to understand.

Tire Pressure, Width and Construction: Narrower tires and higher tire pressures are not always better. If you are using the same tire pressure and have the same amount of vehicle weight above the tires, narrower tires will actually compress more than a wider tire because there is less initial surface contact on the road to absorb the shock. A narrower tire simply has less area to absorb the blow than a wider tire. Like most anything, spreading the impact across a greater area will reduce the effect of the overall impact. This is why 700c wheels with their longer contact patch will have lower rolling resistance than their 650c counterparts with their shorter contact patch. When it comes to rolling resistance, you should pick a tire based upon the quality of the casing and its ability to maintain its shape and choose other components based upon their ability to absorb shock so that the tire doesn’t have to.

Weight: Weight’s relationship to rolling resistance is indirect. On two completely rigid vehicles, the lighter vehicle (bicycle and rider) will have less rolling resistance because it will not put as much pressure on the tires as the heavier vehicle (bicycle and rider) and thus will be easier to lift up and over variances. However, vertical compliance in the wheels and frame changes this completely and the only way to explain how this works is by describing the somewhat complex difference between sprung and unsprung weight, which is found below.

Frame choices and sprung vs. unsprung weight: For those looking to minimize rolling resistance and understand exactly how a vehicle reacts to the ground beneath it, the vehicle’s weight needs to be broken down into sprung and unsprung weight.

I wrote a description of how sprung and unsprung weight works for Softride’s catalog once, so I hope you won’t mind me plagiarizing from myself in an attempt to explain what is not an easy concept. I worked hard to try to figure out a good way to explain this on paper, but didn't succeed as well as I wanted. If you read it slowly and step-by-step, it might make sense.

&Rolling resistance on a bicycle is determined by how much energy is required for it to move over the road. Even fresh pavement is riddled with surface imperfections that slow a bicycle down. Without suspension (vertical compliance), both the rider’s and the bicycle’s weight (an average of 175 pounds for both) is ‘unsprung’ and must be lifted up and over these imperfections for the vehicle to move forward. With suspension, the majority of the weight is ‘sprung’ and imperfections are absorbed by the suspension. On a 'sprung' vehicle, only the unsuspended portion (wheel and lower frame) and a small amount of the rider’s weight needs to be lifted (about 35 pounds for both). It takes far less energy to lift 35 pounds than 175. Thus, to the road, a suspended vehicle feels significantly lighter than an unsuspended vehicle and will have less rolling resistance.

'Sprung' weight also directly reduces tire rolling resistance by keeping the tire contact patch more consistent. Tire rolling resistance is not as much about tire width or tire pressure as it is about consistency of tire contact patch. The more consistent the tire’s contact patch is with the road, the less rolling resistance the vehicle will have. Without suspension there is less vertical compliance and the majority of the vehicle’s weight is ‘unsprung’ and the road imperfections must be absorbed by the rider and tires. Therefore, the vehicle will be slowed as the tire deflects and deforms in an attempt to absorb the shock. Suspension, on the other hand, increases the portion of ‘sprung’ weight the vehicle has. By redirecting the load into the suspension system, the tires are kept from having to deflect as much. The more consistent the contact patch, the lower the rolling resistance and the less energy the rider will have to use to overcome the resistance.”

Conclusion: More vertically compliant frames (especially suspended frames), wheels and components have lower rolling resistance than less vertically compliant frames, wheels and components. The problem is that most highly vertically compliant frames lack much torsional stiffness to allow for climbing. One reason why we often recommend Softride beam suspension and Serotta’s CS, ST and DKS systems to many riders is because suspension allows for torsional rigidity and vertical compliance in ways rigid frames cannot.