I want to remove the texture from my painted walls and was wondering what the best method would be short of replacing all the drywall. The texture is in most places, but not everywhere, and is more in a large swirl pattern in most areas.

Belt sander? Planer?

A belt sander will have to be done very carefully. It tends to sand very quickly and you don't want to sand off too much. A palm sander will work as well. It will probably take a little longer, but you will have more control. Either of these two options will create a lot of dust. Probably the best thing to do, would be to skim coat all the walls with more mud.