To & From The Airport, Tel Aviv-Yafo
My hostel was close to the new central bus station and HaHagana train station, so I had a few options: a shared taxi, a bus or the train. I took the train for 14 NIS (May 2010) and the ride took about 12 minutes to Terminal 3, where Lufthansa had their check-in and drop off bag counters.
Before entering the premises and heading to the ticket booth, there's a security check where they x-ray your bags, like at the airport but without searching you by hand (but take out everything that can make the thing beep or put it in the bag).
I have just been to Israel and rented a car from Shlomo Sixt. I was veery happy with the service that i got. SO if you want to rent car in Israel - I advice you to go for it! - http://www.shlomo.co.il/Car-Rental-Israel/
From Ben Gurion Airport there's a direct Bus to Hayarkon St. (on the coast line and in the center) No. 222.
Or you can take a taxi which will cost you aprx. 20 $.
Busses or a Taxi that Named 'sherut' is all over the city and the costs are cheap as the Buses.
To get to and from the airport the 222 bus leaves about every half an hour, from right outside Ben Gurion, and is pretty easy to find. The journey to the main part of Tel Aviv, where the beach and main hotels/ hostels are located takes about 30 minutes, with stops down Hayarkon Street. If you have a particular destination in mind, sit near the driver and ask him to tell you the nearest stop when you get there.
from ben gourion airport(18 kms) there are many buses, but you will have to change bus outside the airport.Now there is a very nice train in level -1 which starts very early in the morning
From jerusalem there is now a bus every 15 minutes.
There is also a daily bus from cairo(egypt) and from amman(jordan)
If you get to Israel for vacation, i would highly recommend you to rent a car with a gps on Ben Gurion Airport. It is the easiest way of travelling. And if you don't speak any Hebrew, it is by far the best solution to travel in the country.