This node should probably be called Food eaten in Israel instead, since there are very few things that are specifically and only Israeli, as opposed to being Mediterranean, Ashkenazi, Arabic or otherwise originating from one of the many places Israelis come from. Still, out of all these possible cuisines only a few food items have actually become popular, so here's a list of them.

Probably The Only Really Israeli Dish

Ubiquitous Fast Food Who Needs Salads, We've Got Pastes Yemenite Food Largely popularized by the Yemenite fast food chains Nargilla and Nafis. Pester Jester21 or enwhysea to node up more of these!

(Other) Arabic and/or Sephardic Food

See Lebanese food for a list, there aren't many Palestinian specialties that I know of.
Ashkenazi Food Like Your Jewish Mother Used To Make Food-Related Religious Concepts
  • chametz (leavened bread, banned on Passover; Jewish)
  • halal (acceptable; Islamic)
  • kosher (acceptable; Jewish)
  • treyf (not acceptable; Jewish)
Just Plain Evil Additions welcome (where are sabich, lafa, za'atar...?). Le'chaim!