My understanding is that in recent years the use of cluster analysis has gone down and is less respected in a rigorous research setting. Why is this so, and what alternative methodologies are there that may serve a similar purpose?
See most of the final third of http://statweb.stanford.edu/~tibs/ElemStatLearn/. There are also latent variable approaches to undercover classes (e.g., http://onlinelibrary.wiley.com/book/10.1002/9781119970583).
I think many people still like creating clusters/taxa/groups (or whatever they are called in the procedures).
Identifying clusters allows you to do a next step in data mining inside the clusters. This can greatly reduce the amount of required computations. There is a wealth of information hiding in BIG DATA for business applications.