One of the iconic activities in Israel is working "volunteering" on a collective farm: a kibbutz or a moshav. (http://www.kibbutz.org.il...)
Another popular option is to volunteer for work on an archaeological excavation, mostly conducted in summer at a variety of locations. Most Israeli excavations offer college/degree credit for international students. (http://www.ancientneareas...)
While working on a tourist visa is illegal, if you stay at any cheaper hotel in Tel Aviv or Jerusalem, the staff may offer to put you in contact with opportunities to wash dishes or work in construction. Pay is only around $7 an hour, and if caught, you can expect to be deported and blacklisted from the country for a period of no longer than one year.
Israel has many universities which tend to be well regarded by the international community. Special programs for students from abroad are offered by the Rothberg International School (http://overseas.huji.ac.il/) at the Hebrew University (http://www.huji.ac.il/huj...) in Jerusalem, the Lowy School for Overseas Students (http://www.tau.ac.il/overseas/) at Tel-Aviv University (http://www.tau.ac.il/) and the Ginsburg-Ingerman Center for International Student Programs (http://www.bgu.ac.il/osp/) at the Ben-Gurion University of the Negev (http://www.bgu.ac.il/) in Beer Sheva. Also the Technion (http://www.technion.ac.il/) in Haifa.
The International School for Holocaust Studies (http://www.yad-vashem.org...) at Yad Vashem (http://www.yad-vashem.org.il/) in West Jerusalem also offers a variety of educational options relating to the Holocaust or you could also use your time in Israel to study Hebrew. Hebrew school is called Ulpan pl. Ulpanim.
There are even ways to learn Hebrew online from outside Israel - try Hebrew Online (http://www.hebrewonline.com), or Virtual Ulpan (http://www.ulpan.net) if you want some basic background for free.A good starting point for finding more information on study and volunteering programs, can be found on the website of the World Zionist Organization (http://www.wzo.org.il/en/...).
If you are interested in learning firsthand about the social, political and cultural aspects of life in Israel, there are several programs and organizations offering courses, workshops or learning tours, such as: The All Nations Cafe (http://www.allnationscafe.org) in the Jerusalem - Bethlehem area.