Volunteers for Israel is a non-political, non-profit, volunteer organization, associated with Sar-El in Israel. VFI offers two- or three-week programs for volunteers to work on military bases (performing non-combat civilian support duties). in hospitals or at achaeological digs. You pay only airfare and incidental/weekend expenses; your room and board during the work week are covered.
Over 92,000 volunteers from 30 countries have already served.
This sounds like a great way to give of yourself, if you can't yet make aliyah.