I'm trying to find a way by boat from Athens to Tel Aviv and back.
I understand air travel would be cheaper and easier - but I wish to do it more for the experience.
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There are probably no (ordinary) ferries going to Israel.
However, as at January 2010, both Poseidon Lines and Salamis Lines' Piraeus-Cyprus-Israel ferry services remain suspended because of the political situation in Israel, and they show no sign of resuming. A car ferry service for motorists and freight may be operating, though. You can check the latest situation with Viamare Travel.
Some summers has a ferry from Greece via Cyprus to Haifa. However, from the Cyprus ferries page at Varianos travel:
Unfortunately there is no ferry service scheduled between Limassol, Cyprus and Haifa, Israel or Port Said, Egypt for the 2013 summer period. Until 2011 there was a very limited ferry service for passengers connecting Limassol, Cyprus and Haifa, Israel but for 2012 this service did not resumed. The ferry service was only for pedestrians with no vehicles of any kind allowed on board. If it resumes expect that the ferry service from Limassol will not be carrying vehicles again.
However, the situation changes year by year, so it's possible that there will be a new operator trying to open ferry lines.
P.S. You could try to board a Ship to Gaza — the Israeli military may be happy to show you some of the less touristic parts of Israel before putting you on a flight home!
P.P.S. Presently, the overland option via Syria may not be a good idea either.