Following up on Joseph's comment:  Grünbaum and other have pointed out that besides the 13 or 14, there are two infinite families of polyhedra meeting the definition of Archimedean, although generally not considered to be Archimedean.  Why prisms and antiprisms are excluded from the list has never been clear to me.

In any case, this is not just a historical curiosity --- in any attempt you make to classify them, you should run into these two infinite families.

If you use a modern definition, i.e. vertex-transitive, then you will also get 13 others.  And a little group theory can help in the classification.  If you use a more classical definition, i.e. "locally vertex-regular," you will indeed find a 14th.