Suppose you have lots of data with a moderate number of input variables (less than 7, say) and you expect a very complex non-linear function of the data. Examples of this are:
In each case, we already know exactly which features are relevant for predicting the outputs we're interested in, and there are a moderate number of them. We expect the relationship to be non-monotonic and non-linear, but we have plenty of data (although it's noisy) with which to determine the mapping. These are ideal applications for memory based learning because we can easily adjust the amount of localness in the approximator to best smooth out the noise in the data and model the desired relationship.