Do electric cars need friction brakes to stop really fast? If regenerative braking can't stop an electric car fast enough, can't we actively slow it down by applying a reversed voltage to the DC motor?
EDIT: By really fast, I mean in emergency situations where you are about to hit something or someone and want to stop as fast as possible. 
 A: reversing the voltage to the motor while it is running in the opposite direction is regenerative braking. And friction brakes are necessary in electric cars, both to hold them in position while parked and also to hold them in position when stopped on a slope. 
A: 
Do electric cars need friction brakes to stop really fast?

It depends on how fast you're already travelling. Regenerative braking is not as effective as conventional braking methods like friction-based braking at lower speeds. The efficiency of regenerative braking increases with increase in speed whereas it remains fairly constant for friction-based braking.
As you say, we can produce an opposite torque by reversing the polarity of the DC motor to bring it to a stop. But there is always a danger of burning the coils of the motor due to the high surge in the reverse current as the applied current reinforces the induced current. There must be some kind of electronic controllers to limit the current in the coils to prevent such events.
Friction-based braking is effective but it comes at the cost of rubbing mechanical parts which would need regular maintenance or replacement. Regenerative braking can store the energy in useful forms (which can be used later) other than simply dissipating it as heat.  I feel the good way to bring a moving electric car to rest is using more regenerative braking (and less friction-based braking) at higher speeds and more friction-based braking  (and less regenerative braking) at lower speeds.
A: Let me first go over some necessary background knowledge.
Today's cars have anti-lock braking. If the brakes do lock the wheels stops rolling, which gives significant loss of grip, in many cases catastrofic loss of grip. 
About the amount of power that an electric propulsion system can bring to the wheels:
With a high-performance electric car, when the safety features are disabled, hitting the accelerator hard results in a burn-out. Of course, with standard settings the car will dutifully maintain traction control.
Presumably you can put a driving car in reverse and then send maximum power to the wheels. I assume that would result in the wheels spinning backwards, with catastrofic loss of grip.

How much power the battery pack can absorb
Generally the limiting factor to how hard you can brake using purely regenerative braking is how much power the battery pack can absorb. If the battery pack is very large, hence a large overall capacity, the power generated by the regenerative braking can be distributed over a comparatively large amount of battery cells.
If you exceed the rate of current that the battery pack can absorb then the battery suffers irreversible damage. Therefore when you make an electric car brake as hard as possible the regenerative braking is always supplemented with friction braking by the friction brakes.
Dependence on temperature
A cold battery pack has much less capacity to absorb current from regenerative braking. To absorb the power atoms must migrate through a fluid. The lower the temperature of that fluid the slower that migration rate. 
For the batteries: the process of delivering power generates a bit of heat in the battery. Once the battery has reached optimum working temperature the battery management system starts maintaining that temperature. 
