What would happen if two neutron stars collided?

The universe would collapse upon itself.

Time would stop forever in the region they collide in.

Astronomers aren't real sure about colliding or merging neutron stars, but a recent observation of an event known as a gamma ray burst has led many scientists to believe that it may well have been caused by a collision and/or merger between two neutron stars.

Gamma ray bursts release extremely large amount of energy - approximately 10^52 ergs (or 10^45 joules), with the most extreme bursts releasing up to 10^54 ergs. This is the equivalent of turning a star like the Sun into pure energy (using Einstein's famous equation E=mc^2). This is also the amount of energy released by 1000 stars like the Sun over their entire lifetime! In practice, over the few seconds that a gamma ray burst occurs, it releases almost the same amount of energy as the entire Universe!(http://www.astro.caltech.edu/~ejb/faq.html)

The two stars would almost certainly form a black hole, because neutron stars need to be at least 1.44 solar masses (or they would be white dwarfs) and can't be more than about 3 solar masses, or else they collapse into black holes.  So the combined mass of two neutrons stars would almost certainly be enough to form a black hole.