1. Anti-Matter (real)
A trope in science fiction, capable of many amazing and wondrous things, or just turning around as a high octane fuel, anti-matter is relatively simple, it's technically normal matter with an opposite charge. Anti protons are negative charged, anti electrons (aka positrons, ala Lt Data's brain) have a positive charge. When these particles meet each other their charges balance, and all of their mass is converted back into energy. To quote The Fifth Element, Big bada boom. Anti-matter typically appears as a high efficiency high output fuel source, being doled out in a controlled fashion into a reactor where its mutual annihilation with normal matter is converted into usable power. The most famous use of anti-matter is the warp reactor of the Startship Enterprise.
Anti-Matter really likes to explode, and must be contained in a magnetic bottle.
2. Degenerate Matter (real)
An uncommon material in sci-fi, Degenerate matter is matter that has been reduced to it's most dense state. Degenerate matter exists at the point where the position of electrons, protons, and neutrons inside of the atoms composing it are compressed to the point that nuclear forces and the Pauli exclusion principle prevent further collapse. This is the matter that white dwarf stars are made of.
Degenerate matter is incredibly dense, and while not really useful for power production, like depleted uranium, it is fabulous for making ultra dense, but ultra small projectiles.
3. Hyper Matter (fictional)
Much more complicated than degenerate matter, hyper matter is composed of normal matter that has been accelerated above the speed of light. This has converted the fundamental nature of the matter to the point where it exists in a sort of hyperspace. The energy potential of hypermatter is immense, and exceeds the power potential of even anti-matter reactors. Hypermatter is also know as HRM, or hyper relativistic mass.
Hypermatter is the official fuel of Star Destroyers in the Star Wars universe.
4. Dark Matter (real)
Dark matter is non-baryonic matter (not made of protons, neutrons, and electrons) that does not interact with electromagnetic force. This makes it only observable through gravitational interactions and through computer simulations.
Dark matter appears as a mysterious substance and dues ex machine as needed in sci-fantasy.
5. Proto Matter (fictional)
Matter is composed of baryon particles, themselves composed of assortments of quark, giving them their various charges and states. Protomatter is composed of unstable quark, and this instability bleeds over into the physical characteristics of protomatter. The fact that the fundamental charge of a proto-baryon can change in an instant, or that it can switch states means that protomatter can very quickly turn into a massive explosion. The instability of protomatter is infectious, and anything exposed to protomatter in essence becomes more protomatter.
Protomatter was used to fuel the Genesis Torpedo in Star Trek, it's instability lead to the haywire actions across the Genesis planet and it's explosion several months later.
6. Negative Matter (hypothetical/real)
Negative matter has the same electrical charge as baryonic matter, but it's gravitational properties are inverted. An object made of this theoretical material would 'push' with the same force of gravity that a similar mass of normal matter would 'pull'. The potential use of negative matter would be in the creation of engines that would generate free thrust, in exclusion of Newtonian physics.
7. Strange Matter (real)
Strange matter is a soup of quarks, no longer congealed into nuclear matter. Reduced to component quarks, strange matter is even denser than degenerate matter. Neutron stars are hypothesized to be composed of strange matter. Like Dark matter, strange matter is generally used as a dues ex machine.
8. Baryonic Matter (the realest)
Baryonic matter is official name of what we consider normal matter. It is made of Baryons, aka protons, neutrons, and electrons.