Near absolute zero, some materials are superconductors. Other materials are superfluids. Others are Bose-Einstein Condensates.
Is there a complete list of possibilities? Or is this still a research topic?
Actually, superfluidity is describable as Bose-Einstein condensation of bosonic atoms. Superconductors are slightly more complex. Type-I superconductors are well-described by a model in which the electrons (which are fermions) form bosonic pairs which then form a Bose-Einstein condensate. So these three are connected to some extent. All of this on a sidenote.
This certainly still is an active research topic. For example, another possible state of matter was discovered not too long ago: supersolids. I believe the existence of this state is still disputed and I am sure there is no explanation that acounts for all of its properties and behaviour yet.
For a complete list I suggest you take a look at the wikipedia page for states of matter as well as the one for topological order, which is a new kind of order based on topological properties of matter. There is also some useful information on the latter on this physics.se page: Topological phase.