It is agreed upon by physicists worldwide that there are five states of matter. The three common states that occur under "normal" conditions on earth are gases, liquids, and solids. The other two are plasma and superfluids (also known as Bose-Einstein Condensates).
A state of matter is, simply put, a reference to the amount of average kinetic energy of the atoms/molecules that the substance consists of.
A gas is a substance with a relatively low density. It has no definite shape or volume. Examples: oxygen, steam, helium
A liquid is a substance that, like a gas, has no definite shape. However, unlike a gas a liquid does have a definite volume. Examples: water, mercury, bromine, soda
A solid has both a definite shape and volume. Examples: iron, stone, ice
A plasma is a gas in which the particles are stripped of their electrons to form cations. Examples: lightning, stars
A superfluid, or Bose-Einstein Condensate (BEC), is a substance that has been cooled to less than a millionth of a degree above absolute zero (-273.16 C). This state of matter was predicted by Satyendra Bose and Albert Einstein in 1924 and confirmed to exist in 1995.
For the people that are thinking back to their high school chemistry class and how only three states of matter were taught about and used, there is something you need to realize. Physics defines a state of matter, not chemistry. Chemistry is built upon the foundations of physics. Even though only three states of matter are used in chemistry, all five are used in the world of physics. The reason that plasmas and superfluids are not used in chemistry is that there is no chemistry with them. They have their own set of rules. This is because chemistry is the study of how the electrons orbiting atoms interact with other atoms. In plasmas there are no electrons orbiting the atoms so there is not chemistry going on. Plasma physics is used to explain this instead. Superfluids have so little kinetic energy in its particles there is no way for it to react with anything. Chemical reactions must have kinetic energy to take place. The study of superfuidity is used to explain superfluids.
So there are in fact more than three states of matter. Most people that believe this think there are only four states. There are five states of matter defined and used in physics.