* LOX (Liquid oxygen) / RP1 - Actually any hydrocarbon will do from diesel to methane to alcohol. Alcohol was used by the Germans because it was easily fermented, and with 25% water added kept their combustion chambers from melting. The original idea which led to RP1 was to use military jet fuel for rockets, because the military had tons of the stuff, unfortunately jet fuel turned out to be too unrefined for delicate rocket engines. The Redstone was America's version of the V2, using alcohol. The Atlas, the Thor, the Titan I, and the Saturn boosters used LOX / RP1. ISP of 200 - 300.
* Nitrogen tetraoxide / hydrazine - Nasty sounding stuff, and it is. DEADLY POISON! In professional engines it is popular because the combination is HYPERGOLIC, that is the propellants ignite on contact with each other in the combustion chamber. That means that small engines used as thrusters on space craft can have reliable operation without an ignition system. Just open the valves, and the engine fires. Of course if the propellants mix somewhere other than in the combustion chamber you get an explosion, which it is speculated is what happened to NASA's Mars Explorer probe. The largest rockets to use these propellants are the Titan II, the Proton, And the Long March. ISP of 240 - 310.
* LOX / LH2 (liquid hydrogen) - The stuff of Gods. Because the specific impulse of a rocket engine is dependent on the molecular weight of the exhaust products, and because hydrogen has the lowest molecular weight, LH2 is the best fuel for rocket engines. However, there are disadvantages. LH2 is cold, -423 deg F. LH2 is light, only 5# / cubic foot, 1/12 the density of water. This means that the tanks are huge and that they must be insulated. Air will liquefy when in contact with a line carrying LH2, causing huge heat transfers to the fuel, so everything must be insulated. In Space these factors are not problems but LH2 does not make a good booster propellant. ISP of 360 - 500.
* Nitrous Oxide / Propane - There are volumes of information on other propellants, but virtually nothing on nitrous oxide. It is a compressed liquefied gas, and as a nitrogen compound contains a lot of energy. Both materials have been around since Civil War times, but the first experiments with nitrous oxide as a rocket engine oxidizer were done by Leslie A. Skinner in 1936. Some research was done in the 50's but the results are still classified, and I want to get my hands on them. ISP, about 230.
There are two methods of pushing the liquids into the combustion chamber. Use pumps, which are expensive but the tanks can be very light in weight giving maximum performance regardless of cost. Or pressurize the tanks. High pressure in the tanks means heavy tanks which makes pressurized liquid rockets of similar performance to solid rockets, but safer. The Big Dumb Booster design popularized by Arthur Schnitt offsets the lowered performance of the pressurized liquid engine by burning more of the cheap liquid propellant. The ultimate BDB was the Sea Dragon design of Aerojet. This was to be a rocket 550 ft tall, and 75 ft in diameter. The first stage had one engine, 80 million # thrust! The second stage was of course smaller, 14 million # thrust. It was to be launched from the ocean and put a really huge amount of payload into orbit. This super tanker sized rocket never found a market in the limited world of NASA.