Is BLUP a good thing?

After reading the recent publications on the dangers of applying BLUP to
natural populations (Hadfield et al 2010, Morrissey et al 2010) I was
left wondering why it works at all. The latter paper claims that BLUP
has a long and successful history when applied to animal breeding,
but no examples showing its effectiveness were presented.

It depends on how much additional information your model for the latent 
variables carries.  In the genetic case, you have a strong biological 
model for the genetic covariances between individuals given the 
relationships, and in the animal breeding case, lots of data (eg milk 
production in hundreds of offspring of a single prize bull).

Other usages are to give shrunken estimators in an empirical Bayes way, 
but for frequentists ;), or disattenuation of measurement error, or 
estimation of factor scores (they may not actually be called BLUPs in 
other fields).