Micky made some great points about doing research. I'm involved in a different format to consider if you are really interested in pursuing research and helping yourself and your future career. I am working as a research associate in a 7-year pathway at the University of Mississippi in Jackson. It is a position in which one person per year starts off by doing 2 years of dedicated research. Wake Forest and UMass offer similar positions, I believe. During this time, at least in our program, you are enrolled as a graduate student working toward either a Master's or PhD. The spot is filled outside of the match each year and requires mailing your information in separately as an application.
So, you don't necessarily have to do a research fellowship after your residency, and with our program, you are able to complete your degree while you are doing a standard 5-year residency.
For more information about the program and application insructions, check out
http://orthopedics.umc.edu/pathway.html
If you have any questions, please feel free to post or PM me