When (if ever) can ATC order an aircraft to go around?
In real world practice, ATC will have a specific direction for traffic to land and takeoff based on their specific criteria. Regardless of which direction ATC chooses to make the traffic flow, the PIC can choose any runway and/or direction he wishes to land. As long as both parties coordinate and agree, the aircraft can land based on the ATC’s chosen direction or the pilot’s chosen direction. ATC will usually make sure approaching aircraft are kept aware of the wind conditions so that agreement can be made. Either party can decline/deny the approach and/or landing.

An example of this is when aircraft approach our local Class D airfield VFR. They announce that they are inbound with the intention of landing. The PIC will typically then accept whichever runway ATC assigns. When an aircraft approaches IFR, they will typically know which approach and runway they wish to use. The PIC will typically have already negotiated/coordinated this with approach before being transferred to tower. If the aircraft is approaching the airport practicing IFR in VMC, they will negotiate/coordinate the approach and runway to use directly with the tower.

ATC is responsible for traffic separation in their area of jurisdiction. Although, the PIC has ultimate authority over the safety of flight of his/her aircraft, ATC has the authority on whether that flight can include ATC’s physical domain. That domain includes specifically the runway and taxiway surfaces. They can choose whether or not to give an aircraft clearance to use the runway. They can also revoke that clearance for the sake of safety. Some instances where ATC may revoke clearance and call for a go around include:


Reversal of surface winds.  
Windshear.  
Runway incursion by another airplane.  
Runway incursion by a ground vehicle or personnel.  
Runway incursion by an animal.  
Ceilings or visibility going below acceptable runway visual range.  
Closing the airfield due to an accident or emergency.  
Inadequate spacing between aircraft.  
Landing gear issues unnoticed by the landing pilot.  
other safety issues specific to ground or airfield environment safety.


Even before an aircraft approaches the airport for landing, ATC can prohibit them from entering their airspace in its entirety. The aircraft will have to remain outside of the airspace until ATC gives them the clearance to enter. 

All of this can be superseded by the PIC in the case of an actual emergency on the part of the aircraft.