The conventional definition of group speed U=dω/dk is the speed of a wave group composed of collinear wave components. When there is dispersion and refraction, the wave components cannot remain parallel. The U is found to be the apparent speed of the group in the direction of movement of the wavelets within the group. The velocity of a group composed of nonparallel wave components is found to depend upon the directional distribution of the wave components, and it is here termed the geometric group velocity. The geometric group speed G=U cos ϕ, where the angle ϕ is the difference between the direction of the wave group and the direction of the wavelets. For a wave group in which the bandwidth and the directional spread of the wave components are both small the wavelet velocity is nearly equal to the phase velocity of a wave component. The path of a wave packet is found to be given by Snell's law with the geometric group velocity, while at each point along the path the wavelets have a direction defined by Snell's law with the wavelet velocity. The findings are illustrated by using examples of gravity water waves and are confirmed by field observations.