REU (Research Experience for Undergraduates) programs are a way for undergraduates to get some research experience, make contacts and become more involved in their academic community. They're funded by the NSF (National Science Foundation) and sites are located all over the country (as well as some NSF-funded sites abroad).
There are programs in astronomy, physics and many other fields. (Atmospheric Sciences, Engineering, etc.) as well.
Any US citizen or permanent resident who has not graduated prior to the start of the REU program is eligible to apply. A few of the programs (NRAO and NOAO) accept recent graduates. Check with the individual programs about eligability.
Applicants are traditionally Sophomores or Juniors, although Freshmen are welcome to apply to most programs. Applications are typically due at the end of January. It's a good idea to start working on them no later than early December (see the checklist).
The University of Wisconsin provost's office offers research fellowships in a variety of fields. These fellowships will provide you with funding to do a research project with a UW faculty member. The Hilldale Fellowships are open to students with at least junior standing. The deadline for applications is February 16, 2009.
The UW also sponsors an undergraduate symposium, which is a wonderful venue to get some experience presenting your research. Applications will be available through the Symposium website.
WISCI is a peer-reviewed undergraduate research publication, which used to provide opportunities for publishing undergraduate research. This journal hasn't been active recently.
The Undergraduate Research Scholars Program has some projects in the physical sciences which provide opportunities for younger undergraduate students to do research with a faculty mentor.
The Wisconsin Space Grant Consortium offers research awards, up to $3,500, to fund research related to space-studies. Application materials and deadlines have not been posted for the 2009-2010 award year, but last year's deadline for applications was February 4th.
NASA funds many summer schools and institutes to prepare undergraduates for careers in science. This year the Exploration System Mission Directorate is offering the opportunity for students to gain work experience at one of the NASA centers in support of the Vision for Space Exploration: ESMD Higher Education Project
The NASA Academy is a unique experience for people with not only an interest in astronomy, but also earth science, manned space flight, engineering, or space policy and administration. It is a prestigious program with a dedicated Alumni Association. The appliation deadline is in January.
Arecibo Observatory offers a summmer REU program at the telescope facilities in Puerto Rico. Their deadline is typically in early Febraury.
Case Western Reserve University now offers the Carl K. Seyfert Prize Fellowship which will support an undergraduate student for summer research in Cleveland at CWRU. The deadline is 15 February, 2009.
Google is offering the Anita Borg Scholarship to women in computing and science fields.
The nucleus has many summer interships in physics, astronomy and other physical sciences (both domestic and abroad) listed in the summer research section of their website.
The AAS (American Astronomical Society) has a list of REU sites. If you scroll down, this has a good summary of application deadlines and program details. Note that the list is incomplete and there are more sites listed at the NFS REU page.
Jennifer Hoffman's REU FAQ page.
Aaron Geller's links for undergrad researchers.
Snezana Stanimirovic's links for undergrad researchers.
All of these opportunities can help you get a feel for what it's like to do research in the "real world" of academia and can really help you get your foot in the door. Not only will the contacts that you make help you in your future career, but you'll also have experiences which will speak well for you in job and graduate school applications.
If you have any questions, please feel free to contact Snezana Stanmirovic (sstanimi at astro.wisc.edu).