Citation policies: original papers or recent monographs? When referencing previous results, should one cite the original
  paper(s) or a recent comprehensive monograph?


Specifically, in my area of interest (a relatively recent branch of mathematics), in the last ten years, several monographs have been published (by different authors) which cover (virtually) all "classical" results and most of contemporary developements organizing them, putting them in their context, and offering extensive references to the original papers. 

To clarify my position: for the sake of "culture", I've read a few of the original papers in which the results I use most often appear for the first time; however, for the benefit of the reader, I'd rather cite only the most recent (and most comprehensive) source (and possibly point the reader to the additional references therein); in my department, there are researchers following either policies.
Why not cite both?  


  The following theorem is due to Doe [37]; see also [28] for a modern exposition and further background.


Here [37] might be Doe's original paper, and [28] the recent monograph.

Math journals rarely have page limits, so there's no disadvantage to including more citations.  This way you credit the original author and also point the reader to the resource you think will be most helpful.