Wow. You're a college student, and so you have lots of skills. Why not use them during the summer? Better yet, why not do something that will also help you determine what you want to do later in life?
If you want to know what research is like, try doing research in a Research Experience for Undergraduates (REU) program. If you're thinking of graduate school, trying an REU is almost a must! They're lots of fun, and you get paid, too. Application deadlines are mainly in February and March. If you want to know more about whether an REU is right for you, check out this article on the MAA website on Is an REU for you?
REUs receive many many more applications than they have spots, so it's a good idea to apply to at least 6 of them. They also vary widely in structure (for example, whether students work individually or in groups, on similar projects or different projects, with lots of faculty supervision/interaction or very little). If you've been accepted to more than one REU, be sure to ask about the details of the structure if these aspects of your working environment are important to you.
Many programs are restricted to those undergraduate students who will not have graduated before the program begins (that is, they exclude current seniors). The following five programs do accept applications from graduating seniors:
The Park City Mathematics Institute (PCMI) has an Undergraduate Summer School which interacts with the Graduate Summer School and Research in Mathematics programs. (Click on the Summer Sessions tab at the top of the page. They change the URLs regularly.)
NIST SURF is the National Institute of Standards and Technology's Summer Undergraduate Research Fellowship with projects in applied mathematics. There is a Gaithersburg site and a Boulder site (only Gaithersburg currently takes graduating seniors). Applications are made through your undergraduate institution; the person to contact to start the process may be listed here (Gaithersburg) or here (Boulder).
IPAM is the Institute for Pure and Applied Mathematics. It hosts the Research in Industrial Projects (RIPS) for undergraduates and recent graduates.
The National Security Agency has a variety of summer programs, some of which are research-based (such as the very-exclusive Director's Summer Program). They all have October 15th deadlines.
The University of Nebraska-Lincoln hosts the IMMERSE program for students who will be entering graduate school in the fall.
Just for Women:
The Institute for Advanced Study (IAS) hosts an 11-day workshop for Women and Mathematics each May.
George Washington University hosts the Summer Program for Women in Mathematics.
Carleton College hosts the Summer Mathematics Program for Women Undergraduates. It's for rising sophomores or juniors.
About to go to graduate school? Consider the EDGE program for the summer before you start.
Just for non-U.S.citizens:
Very few U.S. summer programs have funding that can be allocated to students who are not U.S. citizens or permanent residents. Those that regularly have such funding include
the Command, Control, and Interoperability Center for Advanced Data Analysis program in the DIMACS family of REUs
the National Institute for Mathematical and Biological Synthesis and hosts a NIMBioS Summer Research Experience
the SMALL REU at Williams College
RIPS at the Institute for Pure and Applied Mathematics
PCMI will fund living costs for students from any country, though only U.S. citizens or permanent residents are eligible for stipends.
Some undergraduate institutions will provide funding for
international students to do summer research or study at other
institutions. Check to see whether you can obtain funding in this
manner. If you can, or if you can otherwise finance travel and
living expenses for the summer, then more summer mathematics
programs will consider your application. Programs that may be able
to make room for an international student who comes with funding
the BYU REU.
If you're interested in trying out the world of industry (business, actuarial, technology, etc.) you might look for an internship.
What if you want some teaching experience? Try looking at middle-school and high-school enrichment programs---many of them hire undergrads to assist with teaching or homework.