Important tasks in cavity quantum electrodynamics include the generation and control of quantum states of spatially separated particles distributed in different cavities. An interesting question in this context is how to prepare entanglement among particles located in different cavities, which are important for large-scale quantum information processing. We here consider a multi-cavity system where cavities are coupled to a superconducting (SC) qubit and each cavity hosts many SC qubits. We show that all intra-cavity SC qubits plus the coupler SC qubit can be prepared in an entangled Greenberger-Horne-Zeilinger (GHZ) state, by using a single operation and without the need of measurements. The GHZ state is created without exciting the cavity modes; thus greatly suppressing the decoherence caused by the cavity-photon decay and the effect of unwanted inter-cavity crosstalk on the operation. We also introduce two simple methods for entangling the intra-cavity SC qubits in a GHZ state. As an example, our numerical simulations show that it is feasible, with current circuit-QED technology, to prepare high-fidelity GHZ states, for up to nine SC qubits by using SC qubits distributed in two cavities. This proposal can in principle be used to implement a GHZ state for an arbitrary number of SC qubits distributed in multiple cavities. The proposal is quite general and can be applied to a wide range of physical systems, with the intra-cavity qubits being either atoms, NV centers, quantum dots, or various SC qubits.