The Oil Rig produces Oil and Passengers; it also accepts Passengers and Mail as cargo. Being the only industry (not counting game-changing NewGRFs) that is constructed entirely on water, it is also only found in the temperate climate. Rigs don't appear until year 1960.
Another specialty about the Oil Rig is that it is a neutral station complete with built-in dock for ships and helipad for helicopters. Every company can transport to and from these facilities as soon as its construction is finished.
Note that some servers running the latest versions of OpenTTD only allow cargo to be transported to or from Oil Rigs via their own neutral stations and nothing else. This means that eventually you will have to use ships to transport oil.
If one company transfers cargo to a rig's neutral station, a second company may pick up the cargo. This causes the first company to lose the payment for the cargo, because the entire payment goes to the company that makes the final delivery.