I just completed an update of our default PCB notes, and spent a good deal of the time on NFP removal.  Much of my research came from the Technet archive, and Werner Engelmaier's whitepaper.   With thanks to Werner, Paul Reid, Wayne Thayer,  Bill Birch, Jack Olson  and others, my conclusion was - it depends.

Trying to balance resin starvation, layer separation, barrel cracking, etc., I came up with:
5.   NON FUNCTIONAL LANDS ON INNER LAYERS MAY BE REMOVED FOR HOLES LARGER THAN n.  FOR HOLES n AND SMALLER, NON FUNCTIONAL LANDS MAY BE REMOVED FROM LAYERS n to n ONLY.   

Instructions for note 5: Do not remove NFPs if copper weight on inner layers is => 2 oz.  Otherwise, NFPs may be removed from inner layers for holes with an aspect ratio <= 4:1.  For holes with an aspect ratio >4:1, remove NFPs from inner 1/3 layers only, DO NOT remove NFPs from top 3 layers and bottom 3 layers.  Examples:  (8 layer, 062” board) FOR HOLES .015 AND SMALLER, NON FUNCTIONAL LANDS MAY BE REMOVED FROM LAYERS 4 TO 5 ONLY.   (12 layer, 048” board) FOR HOLES .012 AND SMALLER, NON FUNCTIONAL LANDS MAY BE REMOVED FROM LAYERS 4 TO 9 ONLY.   

We build class 2, no auto or aero.  We do not do a lot of high power, high layer counts or thick boards.  That might require a different approach.

For far more complete information, find Paul Reid's post (I believe it was on this Technet forum) July 8, 2010.  Also, Werner's whitepaper is an excellent resource.  http://www.engelmaier.com/white-paper.html   The recently released IPC-2221B also deals with the subject.

However you approach this issue, it's important that you make it clear to your fabricator your requirements for NFPs.  Their only concern is ease of fabrication, not reliability, and that often means just a blanket removal of all NFPs.