REU programs supported by the NSF:
REU programs web page at NSF
Current REU Sites in Mathematical Sciences
Search REU sites by research area
NSF REU program announcement & information
NSF REU student participant eligibility criteria

Other useful links:
Summer REU sites listed by the AMS
(Non-REU) Internships listed by the AMS
Programs for undergraduate math majors listed by the AMS
Proceedings of a past conference on REU
MAA undergraduate mathematics conferences
Rose-Hulman Undergraduate Mathematics Journal
Math Rocks
Information for visitors of MSU