Larger-mass neutron stars aren't thought to exist as the gravitational force will be too powerful for degenerate matter to maintain its structure. In other words, the neutron star would collapse and form a black hole.
Although there are hypothetical objects - known as "quark stars" or "strange stars" - predicted to be more massive, creating an intermediate stage between neutron star and black hole, there is little observational evidence that they exist.
So, is there a class of neutron star that has a mass close to two suns, below the threshold of gravitational collapse? Actually, there is.
Discovered last year, PSR J1614-2230 is a millisecond pulsar orbiting with a white dwarf binary buddy. Pulsars are spinning neutron stars that emit beams of electromagnetic radiation from their poles. As the pulsar rotates, we see a flash. In the case of PSR J1614-2230, it flashes at a rate of 317 times per second - it therefore spins at a breakneck speed of 317 times per second.
But that's not what makes PSR J1614-2230 special, it's the fact that its mass has been calculated at 1.97 solar masses - it is the most massive neutron star ever observed.