What would terminal velocity be with no air resistance?

"Or would there be a terminal velocity at all? Would it just keep accelerating until impact?"

Yes exactly, there would be no terminal velocity because the only force on the object would be that of gravity.

Terminal velocity is a phenomena which is BY DEFINITION a condition of the force of fluid drag fully opposing the force of gravity. If there is an absence of a fluid (i.e. vacuum), then there cannot be terminal velocity.

Because of the non-uniformness of gravitational fields, at positions much farther away from the surface of astronomical bodies, there usually *IS* a maximum velocity at which it can fall FROM REST toward that astronomical body. It happens to be numerically equivalent to the ESCAPE VELOCITY, which is the speed at which a free rising object requires to escape the gravitational field of its host body. Granted, you can get higher "entry velocities" by having it thrown from a speed other than rest.

Other than that, all that there could be is the speed of light, as the universal speed limit (as it is called). Usually, the target object needs to be a black hole, for objects to be able to fall towards it at speeds comparable to the speed of light.

The universal speed limit of the speed of light ISN'T based on forces opposing one another, but rather, it is based upon the inertia of an object getting larger with its total energy, since that energy manifests itself as mass.

Terminal velocity happens when the force of air resistance counters the force of gravity.

No air resistance, no terminal velocity (except the speed limit of everything in the universe, the speed of light).