Nitrile: Most common elastomer in o-rings. Aka Buna-N, NBR, acrylonitrile-butadiene copolymer. Excellent resistance to petroleum products, silicone greases and oils, and water. Good compression set resistance, cold flow, tear, and abrasion resistance. Poor resistance to ozone, sunlight, or weather. Temperature range (depending on compound composition) -65F to +300F. Typically 90 Shore A hardness ("durometer").
Silicone: Although this elastomer is not commonly found in scuba o-rings, I have listed it because many divers mistakenly refer to the amber-colored o-ring in some valve faces as silicone when in fact it is polyurethane. Silicone has poor tensile strength, abrasion and tear resistance, but has excellent flexibility properties over a wide range of temperatures. The temperature range is -80F to +450F.
Fluorocarbon: A copolymer of vinylidene fluoride and hexafluoropropylene, fluorocarbon elastomers are highly resistant to deterioration when exposed to many fluids and gases. It also exhibits low compression set, and is highly resistant to heat; it is this property that makes it a common elastomer in Nitrox applications. It is most widely known as Viton, which is a registered trade name of the DuPont Dow Chemical Company. The temperature range is -20F to +450F. Aka FKM or FPM.
Polyurethane: Polyurethane, or urethane, is highly resistant to petroleum products, ozone, and oxidation. It exhibits high tensile strength and is very abrasion resistant. This is the amber-colored o-ring found in the valve face of some cylinder valves. The temperature range is -65F to +200F.
Ethylene Propylene: Commonly referred to as EP or EPDM (ethylene propylene diene monomer), it is a copolymer of ethylene and propylene. It has excellent resistance to ozone and sunlight, compression set, and most solvents. It is non-compatible with petroleum fluids and oils. It is considered inert in the presence of oxygen, and has become increasingly the elastomer of choice for EAN/Nitrox applications. The temperature range is -65F to +300F.
Also used: Neoprene aka CR.