Many, at least in the US. It's not just companies, government agencies also have similar needs due to sunshine and open-access laws.
The alternative to having a document retention policy is to just have employees delete things in an arbitrary manner. It's not just CYA for leaving inconvenient doc lying around, it's also to ensure the proper retention in the event of a preservation order or public records request.
Some companies go way further than others. One place I worked included "notes of a personal nature (eg, birthday cards)" in the retention policy and let us keep them for a week or two before destruction.