There are a number of summer programs in mathematics around the country. The vast majority are sponosred by NSF (the National Science Foundation). A typical program runs for 7-8 weeks, pays you a stipend of 2,000 dollars, and occupies you doing mathematics under a tutelage of a math professor. Often these programs result in published math papers.
Below you will find the list of the NSF-sponsored REU programs. Many deadlines are as early as early February, so I recommend that you send an email or place a call ASAP to the places you wish to apply to get the application packet and more info. I also happen to have descriptions of a few programs written by Harvard students who attended them in the last several years. If you want these descriptions for Indiana, Michigan, and Oklahoma, please let me know.
Another program that some of our students attended in the last several years is PROMYS. It is a summer program for high-schools students, focusing on number theory, and is held at BU. They often hire some of our students as counsellers and teachers. You can obtain more info about PROMYS by sending email to promys@math.bu.edu. If you are interested, I have an article written by one of our students about PROMYS that I can send out by email upon request.
Some students got summer research jobs in the past is The Geometry Center Suite 500 1300 South Second Street Minneapolis, MN 55454. The phone number is (612) 626-0888.
Finally, you can spend a summer or a semester (or even a full year) at the Budapest Math Program in Hungary. It is an excellent program, especially for those interested in combinatorics. I can send more info about it on request. And the Weizmann Institute in Rehovot, Israel, runs another summer science program, though the deadlines for the summer are usually early in December.
Good luck,
Leonid