The Gelfand-Naimark theorem: every commutative C* algebra is $C_0(X)$ for some locally compact Hausdorff space $X$.  

 - The spectral theorem is a corollary.
 - The theorem introduces students to the idea that a ring is a geometric object
 - Certain constructions in topology, e.g. the Stone-Cech compactification, become more transparent.