HOMSIGMAA, the History of Mathematics Special Interest Group of the Mathematical Association of America, conducts annually a contest for the best papers in the history of mathematics by an undergraduate. The winners for 2008 are
Constructivism: A Realistic Approach to Math?, by Mame Maloney of the University of Chicago
2nd prize (tie):
Thinking Inside the Box: Geometric Interpretation of Quadratic Problems in BM 13901, by Woody Burchett, Georgetown College
Jean Le Rond D'Alembert: Biography of a Mathematician, Philosophe, and a Man of Letters, by Cole McGee, Colorado State University-Pueblo
Pathological Functions in the 18th and 19th Centuries, by Mame Maloney, University of Chicago.
These papers may be accessed in pdf format by clicking on the titles.