1947-1949: Israeli War of Independence. When Israel proclaimed itself as an independent state, surrounding Arab nations attacked to try to prevent Israel from establishing itself. The Israelis won and maintained their state and territory.
1956: Suez Crisis. When President Nasser of Egypt nationalized the Suez Canal, Israel along with Britain and France sent troops against Egypt. Faced with international pressure, the British and French withdrew and Israel also eventually backed down.
1967: Six Day War. Fought primarily between Israel against Egypt, Syria and Jordan, with other Arab nations also sending troops. Israel won quickly and convincingly and gained control of much territory.
1973: October War. Also known as Yom Kippur War from the Israeli side, or Ramadan War from the Arab side. Arab nations fought to regain control of at least part of territories lost during 1967 war. Israel won once again and no major territorial changes occurred.
1982: Lebanon War. Israeli Defense Force invaded southern Lebanon, seeking to oust the Palestine Liberation Organization from the region. They did so and established an Israeli security zone in that region.
You could count the First Intifada (uprising) and Second Intifada of Palestinians against Israeli occupation also, depending on how you're defining a "war."
