There are probably hundreds of woods that would make frames out of the 20,000 or so that exist. As long as they are fairly stable when dry. I would guess that oak is probably one of the most common. I've made some out of white birch and white pine. I've also seen them made out of cedar, Douglas fir, other pines, spruce, and walnut. One of the main considerations is whether the wood will compete with the picture for attention. Then it becomes a choice of whether you want to just varnish the frame, or paint or stain it. If you check my downloads you'll see one I made of white birch. The birch was too light coloured to go with the print so I stained it with a water based stain to complement the colours of the print (SamaN brand stain).
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.