We've already talked some about EPC's, but as they are the bread and butter of cluster computation we'll consider them in detail here. If your computational work tends to consist of running a series of more or less independent jobs on your computer, perhaps varying the parameters (or perhaps not), then you are an obvious candidate for a compute cluster. You are the most fortunate of souls, as well, because in most cases you don't much care about the design details of the cluster.
There are many useful tasks that fall into this general category, but perhaps the cleanest example of an EPC task is Monte Carlo calculations and other forms of statistical simulation. This is near and dear to my own heart as it is what I do as a physicist8.1.