First, the program that I went to Germany with is the Congress Bundestag Youth Exchange, or CBYX. 250 American students exchange to Germany every year through this program. The US is divided into five regions, and one organization is in charge of each region. For example, I am with CIEE because I live in the South. You can find more information here: http://www.usagermanyscholarship.org/.
Next is NSLI-Y, which stands for National Security Language Initiative for Youth. This program offers full scholarships to study language for a summer, semester, or year. You can study Arabic, Chinese, Farsi, Hindi, Korean, Russian, or Turkish in a variety of countries. I went to Turkey for two summers through NSLI-Y, and I had truly amazing experiences. Hence, I consider Hilary Clinton my patron. I can speak decent Turkish, which I am determined to continue studying. I have developed a deep love and interest for the country that will stick with me forever. NSLI-Y's website is here: http://www.nsliforyouth.org/nslicms-1.1/.
Finally, YES Abroad is a program that sends Americans on yearlong programs to countries that have large Muslim populations. I know from my connections with this program (I applied, was offered a scholarship to Indonesia, but decided to go to Germany) that it is incredibly valuable because of its role in education about other cultures. You can find more information on the website: http://www.yesprograms.org/yesabroad.
There are more ways to get involved with exchange than going abroad. Hosting is a great experience. From my experiences as a hosted student in Turkey, and as part of an American host family, I recognize the value in this experience. Another way to become involved is to volunteer. I volunteer for AFS (http://www.afs.org/) and it is an incredibly fulfilling experience. The best part is that exchange students are by and large some of the most friendly, intelligent, outgoing, and worldly people you can meet. It is great that I can make my experience more complete by helping others going on exchange.
One place that you can find really great information about exchange is a forum called Cultures Shocked. If you are interested in going abroad or hosting, you will certainly find support here: http://www.cultures-shocked.org/Joomla/forum/index.php.