In 2008, I was awarded a National Science Foundation Graduate Research Fellowship in Computer Science. I found it very helpful to read a few other people's application essays before writing my own. I might be willing to share mine with you if you're applying and promise not to distribute them or anything. E-mail me (rshorey at gmail), and we'll talk about it.
My undergraduate thesis in Linguistics from Swarthmore College from 2006:
Washo Plural Reduplication: A Study of Computational Models (pdf)
The Swarthmore Math department is still hosting my senior conference project on the Gale Shapley Algorithm from 2006 (abstract only as of 2/10). Note that this project does not consist of original research. The assignment was to learn about and report on an interesting mathematical theorem or application.
A paper I presented at 10-ICAL, a conference on Austronesian Linguistics, in Puerto Princesa, Philippines, co-authored with Prof. David Harrison and Katherine Merow (scroll down to Harrison): Sonority Contour Preferences in Philippine Languages.