We report the first experimental generation and characterization of a six-photon Dicke state. The produced state shows a fidelity of F=0.56+/-0.02 with respect to an ideal Dicke state and violates a witness detecting genuine six-qubit entanglement by 4 standard deviations. We confirm characteristic Dicke properties of our resource and demonstrate its versatility by projecting out four- and five-photon Dicke states, as well as four-photon Greenberger-Horne-Zeilinger and W states. We also show that Dicke states have interesting applications in multiparty quantum networking protocols such as open-destination teleportation, telecloning, and quantum secret sharing.