Remote pan/tilt/zoom cameras that aren't expensive
You want a Pan/Tilt head.  Zoom will depend on having a camera that can have the zoom remote controlled and a remote control that can hook in to the zoom.  A pan tilt head can generally either be left sitting on a table or threaded on to a tripod.  They are, however, not cheap.  Expect to spend at least $300 for a cheap one and more if the camera ways more than a couple pounds.