I received an NSF Graduate Research Fellowship Program fellowship in 2011. I applied for the GRFP at the same time I was applying to grad school, so I submitted the application before I was accepted to grad school and heard from both around the same time. I proposed to revise the taxonomy of a group of native bees. The stipend and educational expenses from the GRFP were integral to my success as a grad student. In particular, it allowed me the time and energy to pursue additional avenues that grew out of my original research. I can confidently state that without the GRFP I would not have been nearly as successful and would potentially have dropped out of grad school.
I recently applied for an NSF postdoc award, and I was able to get my hands on some applications from successful applicants. Their willingness to share has inspired me to make my own GRFP application publicly available. Over the years I’ve shared my GRFP application with various people who have asked for it, though that number has probably been less than 10.
When I was putting together my application, my primary guide was the extremely helpful article by Philip Guo: http://www.pgbovine.net/fellowship-tips.htm [Update: that link is now dead and I haven't been able to find it anywhere unfortunately]. In that article, he provides an in-depth guide on why and how to apply for the GRFP and other fellowships. He also provides copies of his application and links to two others. The format of the GRFP application has changed somewhat (from three parts to two) since they and I submitted our applications, but the core concepts remain the same.
The advice I have for people applying to the NSF GRFP is to focus on the personal element of the application and to demonstrate a pattern of determination and curiosity about science in general. One of the main mistakes I see in other people who apply for the GRFP is that they focus almost entirely on their research proposal and neglecting the personal elements. It’s important to remember that the purpose of the GRFP is to nurture promising scientists, not necessarily to fund the best scientific proposals (although these often go together).
With that said, here are the links to my GRFP documents [all in pdf format]: personal statement, previous research, research proposal, and the reviewer comments. One quick note: I accidentally forgot to save the very last versions of my application, so I think there are a couple spelling or punctuation errors that didn't make it into the final version.