Is it possible to use thrust reversers to taxi backwards?
This is called Powerback, most aircraft can do it, but it is not done very often.

In a jet aircraft, the three main problems are:


Reverse thrust tends to throw a lot of debris into the air because the exhaust is deflected to the sides and up and down too. This debris can damage the engine itself, other things on and around the aircraft or injure someone on the ramp. It is less of a problem for aircraft with tail-mounted engines (so DC-9s often used powerback), but that engine configuration is not used as much any more in transport aircraft, as it is less aerodynamically efficient.  
A related problem is that the compressor might suck in its own hot exhaust gases. This might lead to temperature-induced damages in the last (high-pressure) stages of the compressor and health issues for passengers, since the air conditioning system works with bleed air from the compressor.
Reverse thrust is rather inefficient on jet engines, so it uses a lot of fuel.
As Casey mentioned in the comment below, the pilot has to be careful using the brakes during powerback: the main wheels are very close behind the centre of gravity, so harder braking can lift the nose wheel, causing the pilot to lose control and even causing damage to the tail if it hits the ground (“tail-tipping”).


So a tug is both cheaper and safer.

In propeller aircraft, reverse is more efficient and does not throw up as much debris, so it is sometimes used. But a tug is still preferred because transport aircraft don't have any rear visibility, so the pilots can't see where they are taxiing. With tug the driver can see behind the aircraft, and a ground marshaller walks along side each wingtip with an intercom  connected to the plane.

Lastly, since aircraft are able to turn almost on the spot using differential braking and thrust and 180-degree nosewheel steering, at airports with few facilities there is generally enough space around the aircraft to permit the pilot to reverse out easily.