Hitchhiking is very common in Israel. Hitchhiking is done by pointing to the ground with the hand far from the body, instead of raising a thumb.
The most usual way to start an hitchhiking journey is to take a bus out of town, to a junction in your direction. Almost every junction has a hitchhiking spot (the famous Trempiyada), or at least a bus station where drivers can stop. It is very hard to hitchhike from the cities themselves, and inter-urban buses are relatively cheap and can get you to the nearest junction.
Like always, precaution is needed when hitchhiking, although in Israel hitchhiking is a way of life. You will find hitchhikers everywhere. Your best bet for getting a safe ride in Israel is getting into a car with people who know what they are doing. Even still, caution is necessary.
Cities and locations
Note: Israel shares borders with these countries; however, due to hostile relations between the states, it is illegal and probably impossible to cross over to Syria or Lebanon; the West Bank and Gaza should be problematic as well. Egypt and Jordan should be fine.