Researchers at MIT have discovered a new state of matter with a new kind of magnetism. This new state, called a quantum spin liquid (QSL), could lead to significant advances in data storage. QSLs also exhibit a quantum phenomenon called long-range entanglement, which could lead to new types of communications systems, and more.
So we're potentially up to 6 states of matter now? Plasma, gas, liquid, solid, bose-einstein condensate, and this new one.
Off topic a bit, but it's a documentary about the race for absolute zero documenting scienctists trying to reach the coldest temperatures possible. It climaxes in the discovery of the bose-einstein condensate.
This is a more involved question than it first appears. The "simple" answer is that there are three -- solid, liquid, and vapor -- however, Nature is not quite so unimanginative. Some substances have more than one solid phase, depending upon the temperature and pressure. Water, for example, has 13 solid phases at last count. Some liquids, helium for example has two liquid phases -- "normal" helium above about 2.4 K and a superfluid phase below that temperature.