We introduce a class of multiparticle entanglement purification schemes that allow us to purify a large number of entangled states, including cluster states, GHZ states and various error correction codes. We analyze these schemes under realistic conditions and observe that the threshold value for imperfect local operations does not depend on the number of parties for many of these states. When compared to schemes based on bipartite entanglement purification, the protocol is more efficient and the achievable quality of the purified states is larger. We discuss an experimental realization of the protocol in optical lattices which allows one to purify cluster states.