Do high-wingers have dihedral?
High wing planes typically have less dihedral than an otherwise comparable low wing design, because of keel effect: they have more righting moment for a given dihedral angle because the fuselage hanging below the wing increases pressure near the wing root on the low side when a bank induces slip.

The value of the dihedral can be low enough that the wing may look flat (Piper Cubs and Taylorcraft look flat, to me), but if you build a high wing airplane with genuinely zero dihedral, the wing will appear to droop (take a look at period photos of Lindbergh's Spirit of Saint Louis).

Dihedral is present in nearly all high wing aircraft, for the same reason it's present in nearly all low wingers -- because it tends to support or raise the low wing when a bank without coordinated rudder causes side slip.  This produces lateral stability, which in turn makes the airplane easier to fly.