We study the entanglement properties of a class of quantum states that can be generated in arrays of two-state particles (qubits) with simple next-neighbor interactions. Examples of such systems are optical lattices for neutral atoms and arrays of ion traps for charged particles. We show that, by simple interferometric operations, entangled states of large "clusters" of particles can be created which have the following properties: Any chosen pair of particles of a cluster can be projected into a Bell state by local measurements on the other particles. Different from so-called GHZ states, these cluster states have a high {\em persistency of entanglement}, defined as the required number of local (1-particle) measurements to completely disentangle a cluster
