If a torque stops a wheel from spinning, will the wheel continue to move forward without spinning? If a torque applied on a spinning wheel stops a wheel from spinning (on a horizontal surface) will the wheel continue to move forward without spinning?
 A: Rotation and translation are independent motions in general (presence of friction can couple them but you don't mention that in your questions). In that case your question cannot be answered with given information. You can just use Newton's laws to figure our what happens with the transnational motion with the full set of initial conditions given.
A: Assume that the wheel first is rolling (no slip) and then enters a frictionless region. It will then continue rolling. If then a pure torque (no total force in any direction) is applied so that the wheel stops rotating then it will still continue moving (sliding!) in the direction of movement with the same speed as before.
Of course this is a ideal and very hypothetical situation that is difficult to show in reality.
A: Agree with @md2perpe and  @Borun Chowdhury
If the wheel suddenly stops rotating, it will act the same as object sliding on a surface. The coefficient of friction between wheel and the surface will be the same as that of the surface material and the wheel material, and it will start decelerating (assuming nonzero friction) and eventually stop.  
In real life, it is like pulling the hand brake while driving.
A: Depends on the friction between the surface and wheel. See how car brakes work. They apply a torque to the wheel and might cause the rotation to stop, which makes the wheel slide across the surface. This is bad for car brakes, but it might be intended behavior in the situation you are looking at. 
In theory, if you have infinite friction then as the wheel slows its rotation it would also slow its linear speed at the same rate.
A: According to Newton's law of rotation as external torque is applied so the wheel comes to rest and finally wheel stops. 
