Is there any friction between wheel and road?

As many others point out, there is friction present, otherwise the wheel wouldn't grap the surface and pull the car forward. But you are talking about a different kind of friction. There is a possibility of different kinds of friction:

• Kinetic friction, if the wheel ever slides and skids over the asphalt. This is friction between objects that slide over one another.
• Static friction, which is what the other answers talk about. This is friction that holds something still. It always works in the direction that prevents two objects from sliding. The point on the wheel that touches the ground experiences static friction, because it is standing still in that very negligibly small moment.

But

• rolling friction is what you are refering to. Ideally there is no kinetic friction, and static friction only grabs the asphalt and doesn't reduce the speed (on horizontal surface and without wheel torque). All other forces that do work against the wheel rotation (except friction around the axle, as you also point out) are collectively called rolling friction.

Rolling friction happens of several different reasons. For example,

• the rubber tires contract and expand and thus dissipate energy. The energy is taken from the rotation, and this factor counts as rolling friction. Also
• the ground underneath might deform. The deformation costs energy and will as well cause a surface with normal forces that do not act radially (towards the wheel's center) anymore. Such forces will cause torques that might counteract the rotation. See the following picture from this source:

Without rolling friction (in an ideal world), the car will continue to roll and never stop. I believe this is the actual question that you have. Because you are right that in this sense, friction counteracting the motion has been eliminated as you describe.

Without friction between the wheel and the road, you would not be able to accelerate (positive, negative, change of direction).

So it would be impossible to drive a car with zero friction tires. Except you want to use the wheels only to maintain the current state of movement and you do steering and accelerating by other means.

Hovercrafts or magnetic levitation trains use "zero friction" but levitation doesn't move or stop them.