Research:
NSF REU - A list of summer research internships at different Universities and labs around the nation.
NASA Internships - A list of every existing internship, scholarship, and fellowship relating to NASA.
NOAA Hollings - A link to the Hollings scholarship website, which is the premier research/operational scholarship for meteorology undergraduate students.
Operational/Broadcasting:
AMS internships - A list of all of the internships on the AMS website. Almost entirely broadcast positions.
STEP/SCEP, which will be up here soon, as well as any aviation, hydrology, GIS, or other operationally based internships.