There is no EU wide rule, but a small breakdown is found here. Thee are 27 countries only in the Eu, but than you have many more in Europe and near by regions like the Balkans, Est etc..
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Germany is completely dead for overlanding, because both wild camping and off roading are completly forbidden. Yet somehow, when you travel around Europe you find plenty of germans doing it .. :)
Switzerland has extremely high fines for wild camping.
Most Est european countries are ok, also the Balkans, both with wild camping and offroading.
In some countries where wild camping is discouraged there are some ways arround it.
For example in Belgium is not allowed, but if you are fishing, you are allowed to have a shelter, so if you camp near a lake, river and you have a fishing rod in the water - than you are good.
IN France, it depends, basically each bloody village has their own rules, for sure camping on beaches is not allowed, the rest in general is ok... if it is just for 1 night
So it is very complicated, but to break it down, most of Nord and Est Europe are ok , some of the south as well, the rest you really need to pay attention or just go to campsites.
Me personally I prefer more freedom, and less people, so in Germany I stop just for a night maybe at a campsite, since it is too large to go around, on my way to other countries more friendly with overlanders.
Some of the West Europe countries like Netherlands, Germany, Belgium, France are so packed with people that basically there are no more really remote areas left...
So many European overlanders, who prefer remote areas, for longer trips, they go either towards Africa ( a few hours ferry trip from Spain to Morroco ) or towards Est, in the Balkans .. towards Turkey, Asia.. where ever...
You can even reach Africa almost completely by Land with detour trough Turkey and Iran and trough the Middle east.. :)
So plenty of places to go if you have time and money.. :)