The renewal of this 2010 question asks for more recent NSF math grant proposals.

A collection of proposals from 2000 through **2015** is at <A HREF="http://www.math.stonybrook.edu/~bishop/vita/">Christopher Bishop's</A> home page.

This <A HREF="http://people.math.gatech.edu/~dmargalit7/tsr/grants.shtml">site</A> maintained by Dan Margalit has one example of a successful <A HREF="http://people.math.gatech.edu/~dmargalit7/tsr/career.pdf">NSF math proposal</A>, and in addition contains resources on how to write such a proposal (notably the sections on intellectual merit and broader impact).