It seems like at this point it would be game over, since the spinning rotor is the only thing keeping it in the air. Is there any way to land a helicopter in this condition without crashing?
Helicopters are able to do something called autorotation if all thrust is lost.
(Look in particular at the direction of flight arrows. Remember there's a lift vector coming of the blades as well in both cases.)
Basically, the collective is decreased immediately when thrust is lost for whatever reason. This allows the airflow coming through the blades to push them around, like a reverse windmill in a way, keeping the blades spinning. This also generates lift, keeping the helicopter generating some lift (while descending of course).
Once the helicopter reaches ground, the pilot will pull up. Since the blades were spinning a bit faster than needed for a hover since he was flying forward the whole procedure, he simply pulls up and levels out carefully close to the ground until the helicopter touches down.
This being said, you have to be careful, since if you're flying to slow you can't pull it off.
This dangerous conditions are shown in a height-velocity diagram as is seen below, in this case apparently from an R44.
Here's a little video to get an idea of how it looks for the pilot: http://www.youtube.com/watch?v=yNWjW6yORyg
Autorotation is often time critical and has to be done right as there's only one shot and as such is practised by pilots on a regular basis.
All extracts in this section are from "Helicopter Emergencies and Hazards" by the FAA, an excellent and very extensive publication on the topic.
Many helicopters have more than one engine driving the rotor system. On those, losing an engine is probably less serious than it would be in a single-engine craft.
All helicopters that I'm aware of are capable of autorotation. In an autorotation, the pilot uses the air rushing up through the rotor disk to keep the blades spinning. This involves changing the collective angle of attack of the blades to near zero to minimize drag, plus some other control inputs.
While doing this, the pilot is trading potential energy (altitude) for kinetic energy (keep the rotors spinning).
Immediately prior to landing, the pilot changes the collective angle of attack of the rotors back to the normal "push air down" setting. This rapidly slows the rotors, but if done correctly there's enough cushion to land the vehicle.
For a much more detailed description of how to execute an auto-rotation landing, see How does a helicopter pilot execute an auto-rotation landing?
Per FAR 61.87(f)(15), A student pilot who is receiving training for a helicopter rating must receive and log flight training for the following maneuvers and procedures:
... (15) Simulated emergency procedures, including autorotational descents with a power recovery and power recovery to a hover;