When you think of Israel and airplanes, you usually think of El Al (The Israeli National Carrier, http://www.elal.com ) but there are more airliners that are Israeli. Arkia Airlines operates flights from between Israeli cities:
Haifa
Ste Dov (Tel Aviv, Northwest Side)
Ben Gurion (Eastern Tel Aviv)
Eilat
Rosh Pina
Jerusalem (This airport is closed because it's near the Palestinian town of Ramallah)

Arkia also flies to several European countries from TLV. For more information on Arkia go to http://www.arkia.com

Israir is another airliner that operates flights to the same airports, and European flights from TLV as well. For their official website, click here http://www.israir.co.il
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Now this comes to another question...
Are there any non-Israeli airliners that serve airports in Israel except Tel Aviv or Eilat? The answer is yes. A Lufthansa airplane was seen at Haifa airport a few months ago and I believe they fly to Haifa but I'm not sure. Any Lufthansa experts know? Bitte? Dank!