The effects on synchronization and spatiotemporal patterns in coupled neurons are investigated. Firstly, noise-induced and noise-enhanced synchronization can be observed in coupled neuronal systems as the noise level attains suitable values. Secondly, the collective behaviour of a square lattice Hodgkin-Huxley neuronal network model with white noise is studied. It is shown that when the noise level reaches an intermediate value, the Hodgkin-Huxley neurons in this square lattice will exhibit an ordered circular structure. However, as the noise level increases, the ordered circular structure is distorted, and eventually totally destroyed when the noise level is high enough. This manifests the existence of spatial coherence resonance in the network and may be instructive to understand information processing of neural systems in the presence of noise.