For some months already Israel has decided to no longer stamps passports at arrival or departures in Ben Gurion International airport. The stamps were a concern for travelers who wanted to include future plans to visit countries that may impose some kind of restrictions for those who have previously visited Israel.
The Israeli stamp was especially problematic when intending to visit places such as Lebanon, Syria, or Saudi Arabia. There were a lot of fears about being rejected when trying to enter UAE or Egypt with an Israeli stamp in the passport, but this never has been the case.
The procedure of arrival continues to be the same, it is good to keep in mind that airport security is really tight in Tel Aviv, and it is not infrequent to see police agents dressing like civilians stopping people to interrogate them before one has even reached the immigration control area. Once one gets to the arrivals hall the officer takes the passport and he/she may or may not ask some routine questions such as how long one is intending to stay. Then they put the passport in the electronic reader and they print a little card with all personal information, picture included. It is very important to keep this card safe at all times since one has to present it at departure and some times at check-in in hotels. I am not sure what it will happen with passports that are hand made, (containing no electronic strip) it is better to call ahead and ask the Israeli Embassy before the trip.
The normal feeling is that security is even tighter when leaving Israel than when arriving, so it is good to leave extra time for the normal procedures at the airport. Once again the departure immigration officer puts the passport in the electronic reader and they print another little departure card that is handed back with the passport and the arrival card.
It is good to keep in mind that countries that give some problems to passport holders with Israeli stamps still can be suspicious and give a hard time to travelers that have stamps in their passport from the land border crossings with Jordan or Egypt.