Why do a second PhD in a "neighboring" discipline? I recently received an application for a PhD position from someone who is already working as a postdoctoral associate. The difference in fields is not particularly large—I work in chemical engineering and materials science, while the applicant originally is coming from computational chemistry. 

So the obvious question is, why would someone want to pursue a second doctoral degree when they already have one in a related field, and why would I, as a potential advisor, want to consider someone interested in doing this? (For instance, it seems obvious that the person wouldn't likely need as much training as a novice, but there would also be the challenge of trying to find such a person gainful employment afterwards.)
I've seen two reasons for this.  The more worrisome reason is the one mentioned by EnergyNumbers in the comments, namely that some people just collect degrees.  In particular, they may feel having two Ph.D.s would look exceptionally impressive, or they may be unable to settle on a specialization, or they may feel that getting another degree is somehow preferable to getting a job.  These could be legitimate as personal desires, but they are counterproductive for a research career.

The other reason is to recover from a bad career start.  Sometimes someone's grades keep them from getting into a good graduate program, or they face other constraints (geographical or financial) in their choice of programs, or they fail to connect well with their advisor.  They may eventually get a Ph.D., but not under good circumstances, and a second Ph.D. might lead to a much better career.  The difference between this case and the first case is that these students don't actually want a second Ph.D. as such.  They regretfully feel they need one to achieve their career goals, but they wish it had been their first and only Ph.D.

Recovering from a bad start is a less worrisome reason to seek a second Ph.D., but of course the challenge is figuring out which students have moved beyond their past difficulties and which have not.