In practice, the process rarely proceeds in a purely linear fashion. Iterations, by going back to or adapting results of the precedent stage, are common. The Waterfall model is considered old-fashioned or simplistic by proponents of object-oriented design which often uses the spiral model instead.
In the original article, Royce advocated using the model repeatedly, in a iterative way. However, most people do not know that.
See also: Project lifecycle, Spiral model, Chaos model.
This article (or an earlier version of it) contains material from FOLDOC's article on Waterfall Model, used with permission.