So long as a surface is primed properly, oil paint can be used on just about any surface. However, for the sake of protecting the durabiity of the artwork and to avoid cracking or damage, the main kinds of surfaces artists have narrowed down to are panels of wood and stretched canvas. There are different types of wood and canvas to choose from but in all cases the surface has to be prepared primed, also called a "ground", and the most common type of ground is gesso.
The most common type of canvas cloth used for painting are linen and cotton, with linen having a finer texture which allows for finer details without the texture of the canvas affecting brush strokes. Most often when painting on canvas, the material is first stretched onto pieces of wood called "stretcher bars" and then given multiple coats of gesso as a primer. For added archiavility and durabiity, a glue-like medium is used in the initial coat before the gesso layers are added.
As for wood panels, common choices might be playwood, particleboard or fiberboard. You might as why not solid wood as an option? That's because when one side of a solid but thin piece of wood is prepared with a gesso ground, it keeps moisture from penetrating that side of the board, so in different humidity situations the other side of the board will stretch and shink unevenly from the front, causing warps and potential cracking. Pressed wood allows for moisture to "breath" through the wood more evenly and resists warping. There are, however, very specific kinds of solid wood board which can be used that resist warping - e.g. well-seasoned, quarter-sawn and air-dried woods, which also have matching grains front & back to help further minimize uneven warping, but their cost compared to pressed woods may be prohibitive.
Lastly, it is possible to use oil paint on metal surfaces such as copper or aluminum but much greater care needs to be taken when preparing those surfaces.
