Internship information to get you started:
ASA website
http://www.amstat.org/education/internships.cfm
http://netlib.bell-labs.com/cm/ms/departments/sia/employment/intern.html
Urban Institute
http://www.urban.org/about/careers/internships.cfm
Economics internship site (some of these really want a statistician)
http://www.missouri.edu/~econsr/internships.htm
ETS
http://www.ets.org/research/fellowships.html
Westat
Person in charge of the internship program is Lloyd Hicks (HICKSL1@WESTAT.com) I was told that they have about 3 interns every summer and you would contact Hicks directly.
Stata
http://www.stata.com/internships/
http://www.rand.org/about/edu_op/fellowships/gsap/
Mathematica (This one says it is looking for social scientists. However, much of Mathematica’s work is in sampling and survey methods, and they employ many statisticians, so it may be worth an inquiry)
http://www.mathematica-mpr.com/employment/summerfellow.asp
Bureau of Justice Statistics
http://www.ojp.usdoj.gov/bjs/jobs.htm
National Opinion Research Corporation (This one says social
science research, but is actually a high quality survey research organization
affiliated with
http://www.norc.org/careers/summer+internship/
Gallup (Select Scholarships/Internships on Job Field drop down list) http://www.gallup.com/careers/search/
A “statistics” job consolidator site – not just internships
http://www.aftercollege.com/groups/listings.asp?id=707192983
These aren’t specifically statistics, but are local and we have had students/graduates who have worked there:
Southwest Airlines
http://www.southwest.com/careers/internships.html
Mary Kay
http://www.marykay.com/mkjobs/jobslanding.aspx
Neiman Marcus
http://www.neimanmarcuscareers.com/index.shtml