It doesn't seem like riding a broom requires a wand, though IIRC they do have to say "Up!" to ...animate (right word?) the broom. Does this qualify as magic that only wizards can do? If so, could a Muggle ride a broom after it was animated?
I guess this would apply to most magical transit; Floo powder, Apparition (at least side-along Apparition), Thestrals, magic carpets, etc do not seem to require a wand to work. If a Muggle had access to a broomstick (it doesn't seem as if any old broom will do) or Floo powder, could they use these methods despite being Muggles? Is there any canon evidence for either answer out there?
(This is my first question on here, so I hope it's appropriate and ok to ask this. Thanks!)