The coefficients of friction Philo provides for tyres won't help you. What you need for the calculation you're interested in is the rolling friction, or rolling resistance. The relevant equation is Torque to overcome rolling resistance (T) = Vehicle speed / rotational speed (ω) * rolling resistance. Estimation of the rolling resistance, as you might guess from the other posts, can be a complicated affair but I expect at LEGO scales it mostly depends on the tire and the vehicle weight. -Brian A.
Thanks @jodawill for pointing out that the rolling resistance in the above equation is resistive force, not the coefficient of rolling resistance. For a rigid tire on a rigid surface, this equation reduces to T = r * F, where r is the tire radius and F is the force at the axle pushing the vehicle forward. The coefficient of rolling resistance, Crr, is defined from F = Crr * N, where N is the normal force the axle exerts on the tire (i.e. the weight on the wheel). If you make these two substitutions (the first one being dubious), the original equation becomes T = Crr * r * N.
That gives us an easy way to determine the Crr, with a caveat I'll give later. I'll call it a "coast-up test" because it's a coast-down test in the opposite direction. Build a simple test vehicle with all the same tires and no drive train. Put it on an inclined plane (i.e. a board). Measure the height of the vehicle off the ground level. Let the vehicle go and time how long it takes to reach the bottom. Using the standard acceleration equation s = 1/2 * a * t^2, where s is the length of the plane, a is all the accelerations experienced by the vehicle (assumed to be constant) and t is the time to cover distance s, it can be shown that the definition of Crr, Newton Laws and this last equation can be combined to h / s - (2 * s) / (g * t^2) = Crr, where h is the height and g is the acceleration of gravity. Now you have a coefficient of resistance, which is dominated by the rolling resistance. You can then apply this using T = Crr * r * N to any vehicle.
Now for the caveat. Crr is going to increase with torque, especially for softer tires, and in this coast-up test the torque is minimal. There are more caveats. It only applies to the surface you tested on. Carpet, wood, and gravel will give you different Crr values. Crr may also increase with speed. Finally, the equation neglects the momentum gained by the tires which will decrease the value of t (increasing the apparent Crr), so it would be good if the body of the test vehicle is much heavier than the tires. Probably at least by a factor of 10.