A big part of research is communicating with others in the field. If you have researched and written a paper, there are several forums for you to present and publish your work to continue the conversation.
Most large national professional organizations (like American Sociological Association, American Psychological Association, Society for Research on Child Development, etc.) accept poster and oral presentation abstracts from scholars at any level, including undergraduates. Many undergraduates have successfully presented at these large national conventions - especially in poster format - so don't be shy and go ahead and submit if you have done work of which you are proud!
But here are some smaller venues and/or venues specifically focused on student work.
Academic Commons at Columbia University: Students, faculty and staff can electronically publish their scholarly work in a free, digital space.
Annual Biomedical Conference for Minority Students: An annual conference at which minority students doing research in biomedical fields(including the social and behavioral sciences in health) can present their research. Usually held in late November.
Council on Undergraduate Research: A list of undergraduate research presentation opportunities for different subjects put forth by the Council for Undergraduate Research, which strives to support and promote high-quality undergraduate student-faculty collaborative research and scholarship.
Eastern Economic Association: The EEA hold special sessions for undergraduate researchers to present their research at the Annual Meeting held Boston March 9-11.
Eastern Psychological Association: Undergraduate psychology papers can be submitted for presentation at the EPA's Annual Meeting in New York City.
Eastern Sociological Society: Undergraduates can submit sociological paper abstracts for posters that will be displayed at the ESS Annual Meeting in Boston. Papers are also accpeted for presentation during the regular paper session. Deadline for the 2013 Annual Meeting was December 15.
ICSPR Research Paper Competition: Research paper competition for papers that analyze data from ICPSR. Cash prizes are available for top papers.
Journal of Politics and Society: Columbia's Journal of Politics & Society publishes undergraduate work on a range of social science topics. A print copy of the Journal is published twice a year. Deadline for the Spring 2013 edition was January 1, 2013.
National Conference on Undergraduate Research (NCUR): A conference specifically dedicated to presenting undergraduate research. Scroll down to where it says "Student Events."
Northeastern Political Science Association: Political Science students can submit their work for presentation an the Northeastern Political Science Association. Students must be sponsored by a faculty member for consideration.
Undergraduate Journals and Conferences Directory: Contains a directory of journals and conferences that focus on publishing and presenting undergraduate work in a variety of fields.