A series of experiments have been undertaken on the fragmentation of multiply charged ammonia clusters, (NH3)(n)(z+), where z <= 8 and n <= 850, to establish Rayleigh instability limits, whereby clusters at certain critical sizes become unstable due to Coulomb repulsion between the resident charges. Experimental results on size-selected clusters are found to be in excellent agreement with theoretical predictions of Rayleigh instability limits at all values of the charge. Electrostatic theory has been used to help identify fragmentation patterns on the assumption that the clusters separate into two dielectric spheres, and the predicted Coulomb repulsion energies used to establish pathways and the sizes of cluster fragments. The results show that fragmentation is very asymmetric in terms of both the numbers of molecules involved and the amount of charge each fragment accommodates. For clusters carrying a charge <=+4, the results show that fragmentation proceeds via the loss of small, singly charged clusters. When clusters carry a charge of +5 or more, the experimental observations suggest a marked switch in behavior. Although the laboratory measurements equate to fragmentation via the loss of a large dication cluster, electrostatic theory supports an interpretation that involves the sequential loss of two smaller, singly charged clusters possibly accompanied by the extensive evaporation of neutral molecules. It is suggested that this change in fragmentation pattern is driven by the channelling of Coulomb repulsion energy into intermolecular modes within these larger clusters. Overall, the results appear to support the ion evaporation model that is frequently used to interpret electrospray experiments.