Dissociative recombination (DR) of water cluster ions H(+)(H(2)O)(n) (n=4-6) with free electrons has been studied at the heavy-ion storage ring CRYRING (Manne Siegbahn Laboratory, Stockholm University). For the first time, branching ratios have been determined for the dominating product channels and absolute DR cross sections have been measured in the energy range from 0.001 to 0.7 eV. Dissociative recombination is concluded to result in extensive fragmentation for all three cluster ions, and a maximum number of heavy oxygen-containing fragments is produced with a probability close to unity. The branching ratio results agree with earlier DR studies of smaller water cluster ions where the channel nH(2)O+H has been observed to dominate and where energy transfer to internal degrees of freedom has been concluded to be highly efficient. The absolute DR cross sections for H(+)(H(2)O)(n) (n=4-6) decrease monotonically with increasing energy with an energy dependence close to E(-1) in the lower part of the energy range and a faster falloff at higher energies, in agreement with the behavior of other studied heavy ions. The cross section data have been used to calculate DR rate coefficients in the temperature range of 10-2000 K. The results from storage ring experiments with water cluster ions are concluded to partly confirm the earlier results from afterglow experiments. The DR rate coefficients for H(+)(H(2)O)(n) (n=1-6) are in general somewhat lower than reported from afterglow experiments. The rate coefficient tends to increase with increasing cluster size, but not in the monotonic way that has been reported from afterglow experiments. The needs for further experimental studies and for theoretical models that can be used to predict the DR rate of polyatomic ions are discussed.