NASA offers paid undergraduate and graduate level internships in a variety of disciplines from business and finance to biology, chemistry, physics, earth and life sciences, and engineering. The deadline has recently been extended to March 1, although offers may begin going out February 2nd. Students are encouraged to apply by February 1st.
Please visit http://intern.nasa.gov to complete your application and apply for up to 15 opportunities with a single application. There are currently over 200 opportunities available.
For tips on the internship application: http://www.youtube.com/watch?v=4saIcVc62-8
For tips on searching for and applying to internships and fellowships:
https://intern.nasa.gov/solar/web/public/main/index.cfm?solarAction=video