What would be an example of a currently possible overland route from Europe to Israel?

The long way around:

It may be possible to get to Israel overland from Europe via a ridiculously circuitous route that avoids the current (2016) trouble spots in Syria, Iraq, Libya, and Saharan Africa. The first step is to get to Iran, by one of the following routes:

• From mainland Europe to Turkey, thence west to Iran, crossing the border into Iran either near Gürbalak, Kapiköy, or Esendere.

Note that as of this writing (July 2016), the U.S. State department does not recommend travel to southeastern Turkey, which would eliminate the second and third of these border crossings. If you wish to avoid Turkey altogether, you could also enter via Azerbaijan:

• From mainland Europe to Russia, and south into the Dagestan region of Russia.
• Cross into Azerbaijan and continue south.
• Cross the border into Iran, either at Astara or Bilasuvar.

Once you have done this:

• Take a ferry across the Persian Gulf. Three useful routes exist. The Bandar Lengeh–Dubai and Bandar Abbas–Sharjah routes will deposit you in the UAE. There is also a ferry from Khorramshahr to Kuwait City, though it is passenger only and you will need a vehicle for the next step.
• Obtain a driving transit visa for Saudi Arabia, and drive from the UAE to Jordan (and thence to Israel.)

I am honestly not sure whether this is actually possible. The two steps that I have italicized above may be problematic, depending on one's citizenship. Also, you might have to be cagey with various border officials in Iran, UAE, and Saudi Arabia about what your final destination is. There's the issue of whether you could successfully bring a vehicle along with you the whole way; without that, one would have to rely on long-distance buses, which I suspect would be difficult (particularly in Saudi Arabia.) And given the current state of relations between Saudi Arabia & Iran, it may be difficult to get a Saudi transit visa after visiting Iran.

I don't expect that anyone would actually do this; I was just amused that it might actually be possible.

The title and the body ask different questions.

Strictly overland is going to be very problematic. It would require passing through at least one of Iraq or Syria. Large parts of both are currently under the control of ISIS and Syria currently has multiple factions fighting for control. Possibly you could edge your way round the east and south of Iraq into Jordan but I doubt it would be an easy trip.

On the other hand if you just want to get there without flying then there are Mediterranean cruises that stop off in Israel http://www.cruisecompete.com/itins/msc_fantasia_cruises_bcdacdfc.html

According to their website, in 2016 Salamis Cruise Lines operates an occasional roundtrip cruise from Limassol, Cyprus to Haifa, Israel and back. You would need to contact them to see exactly what happens if you decided not to get back on the ship (assuming you want to visit Israel for more than a day), and it's probably substantially more expensive than flying (especially if you're throwing away half of the round trip and/or traveling alone). But trying to work with them is probably your best bet.

Other cruise lines occasionally make stops in Israel as part of Mediterranean trips, but those would generally be longer itineraries, while the Salamis trip might theoretically work better as an expensive ferry.

Getting to Cyprus from elsewhere in Europe without flying takes a bit of effort, but The Man in Seat 61 has some tips as always.

In 2015 no passenger oriented ferries operate to/from Israel, however some cargo companies will take passengers as well. Grimaldi certainly does, I am not sure whether anyone else does. It's significantly more expensive than flying to Israel.