With an Israeli stamp in your passport, Syria and Lebanon will definitely be a no go. Even if you have exit and entry stamps from a crossing such as Aqaba, this may also cause you to be denied entry to these countries. I had Sharm El Sheikh stamps in my passport when I entered Syria and it took them quite some time to establish I had only been to Egypt.
Other countries that could be difficult to enter with an Israeli stamp include Saudi, Iran, Sudan and UAE.
I'm a British citizen with a passport full of Arab stamps, and whilst I wasn't denied entry into Israel, it did incur a lot of waiting around and questioning.
If you're going to go to Israel, cross over the Allenby Bridge (when entering and exiting), as you're not stamped in or out of Jordan. Although you'll have to request the lemon sucking immigration official at Israel's border not to stamp you, which means more questioning and waiting around, but at least your safe to travel as you please afterwards.
Enjoy!