Question: Can you run a [BLDC motor](http://en.wikipedia.org/wiki/Brushless_DC_electric_motor) backwards without damage?

Is it OK to drive a model airplane BLDC engine backwards while landing, so it gets a little "reverse thrust" and come to a stop a little quicker on the runway?

Is it OK to drive a model helicopter BLDC motors backwards so it can hover upside-down?

Or do I need to design the hardware so that it never drives the motor backwards, under any circumstances, no matter what the pilot on the ground does at the transmitter?

Answer: 
Yes, you can drive a brushless DC motor in both directions.

See, for example, the [On Semiconductor MC33035](http://www.onsemi.com/PowerSolutions/product.do?id=MC33035PG) brushless DC motor control chip, which has a pin to control direction.

Here's a little explanation from p. 9 of [the datasheet](http://www.onsemi.com/pub/Collateral/MC33035-D.PDF):

> 
> The Forward/Reverse input (Pin 3) is used to change the
>  direction of motor rotation by reversing the voltage across
>  the stator winding. When the input changes state, from high
>  to low with a given sensor input code (for example 100), the
>  enabled top and bottom drive outputs with the same alpha
>  designation are exchanged (AT to AB, BT to BB, CT to CB).
>  In effect, the commutation sequence is reversed and the
>  motor changes directional rotation.
> 
> 
> 

I believe you do have to be careful about "shoot-through"-- if you're trying to switch the direction of current flow in a winding, you have to be sure to turn one set of FETs off completely before you turn on the other set, or you may inadvertently short your power supply.

You might google "adaptive gate drive" or "dead time" for more details.
Thrust on helycopters is controlled by varying the propeller pitch, not the motor speed/direction. In an helycopter, the main rotor motor turns almost always at the same speed. 

Inverted hovering needs a special designed [swash plate](http://en.wikipedia.org/wiki/Swashplate_%28helicopter%29) that allows positive and negative blade pitch. 

For the original question, yes, you can drive a brushless dc motor in both direction. 
Stopping it quickly (with a propeller connected to it), change direcion to the thrust, and keeping your plane on the track, is another story :-)