Be aware that security is tight at Ben-Gurion airport. You will be questioned on arrival into Tel Aviv.
When you depart you will be designated a security officer ( usually a young soldier), who will personally take your luggage apart item by item. So don't attempt to take anything you shouldn't.
This also applies if you leave by boat from Haifa.
If you have overstayed your 3 month visa be prepared to explain why. If the overstay is only a matter of a week or two you will usually be okay. I knew some travellers who had overstayed several months and had a ban put on them. One Australian girl I knew was banned from returning to Israel for 9 years, although five years seems to be a more common time ban.
If you have stayed a while in Israel you may be asked about any associations you have made in this time. Be careful if you keep a travel diary as it will probably be read.
Although this is intrusive it is best to grin and bear it, as any attempt not to comply may be misread by the officials.