Speakers are also made out of just about any type of material you can imagine as well.
Wood, MDF, HDF, Plastic, Composites and even metal speakers. Most speaker cabinets are made out of MDF (Medium Density Fiberboard) or wood. You might think that wood cabinets would be superior to MDF cabinets but it is often not the case.
MDF if made correctly is often stronger and more stable than wood and can be more cheaply finished with beautiful wood veneers. This means you have a greater choice of looks and finishes since a cherry veneer is far cheaper than a solid cherry speaker.
Because MDF is easy for manufacturers to work with it's also more cost effective and delivers a more affordable product to your average consumer. This is not to say that solid wood cabinets are a bad thing, just that there is often no advantage to using it in speaker design.
Solid wood will also color the sound. Just like you can purchase acoustic guitars with different types of wood tops that offer varying colorations, wood will change the sound of the speaker.
MDF will also be more resistant to changes in temperature and moisture, offering a more stable sound over time.
As for other materials, plastic and metal, I'd personally shy away from these outside of small blutetooth speakers.