If you intend to visit Israel, the West Bank or Gaza as part of a longer journey in the region, you need to bear in mind that it is the official policy of almost all Middle Eastern and North African countries (exceptions include Egypt, Jordan and Morocco) to refuse entry to people who have evidence of a visit to Israel in their passports. “Evidence” includes not only Israeli stamps, but also Jordanian entry or exit stamps from the border-posts at the Sheikh Hussein/Jordan River Bridge, the King Hussein/Allenby Bridge and the Wadi Araba/Yitzhak Rabin crossing (Aqaba–Eilat), as well as Egyptian stamps from the border-posts at Taba (near Eilat) and Rafah in northern Sinai. Visas issued in Israel for travel to any country and flight itineraries that specify Tel Aviv (or TLV) will also bar you, as will anything in Hebrew discovered in your belongings.
We’ve had some reports of travellers holding Israeli stamps getting into certain countries (Tunisia, Oman and the UAE, among others) without any difficulty, but this can’t be relied upon. Syrian and Lebanese officials are the least flexible in this regard.
The best advice is to construct your itinerary so that you visit Israel last, after Syria and the rest. Alternatively, you can apply in your home country, well in advance, for a second passport: many countries issue these to people travelling around the Middle East as a matter of routine, but it’s then up to you to ensure that your tally of entry and exit stamps in each passport adds up, and that you don’t hand the wrong passport over to the wrong border official.
If you hold only one passport, there is no foolproof method of avoiding a giveaway stamp. If you’re feeling lucky, and you’ve entered Jordan by air, sea or across the land borders from Syria, Iraq or Saudi Arabia, then you could try using only the King Hussein (Allenby) Bridge to cross from Jordan to the West Bank and back (while making sure that your Jordanian visa does not expire in the meantime). At this bridge Israeli and Jordanian immigration officials will usually stamp you both in and out on a piece of paper if you ask, thus avoiding any permanent evidence of having been “on the other side” (as many travellers refer to Israel, to avoid detection by eavesdropping officials). However, the success of this depends on not running into an official who decides to stamp your passport regardless.
It’s a well-known ploy of travellers who have unwittingly acquired evidence of a visit to Israel to lose their passports deliberately in Egypt or Jordan and apply for new ones from their embassies. However, an unused passport issued in Cairo or Amman is as much evidence to some consular officials of a visit to “Occupied Palestine” (as Syrian visa application forms put it) as a border stamp. Even if the loss of your old passport was genuine, you may still find yourself refused entry to certain countries on this suspicion alone.