Originally Posted by stut
Many car hire companies are less than happy for you to take your hire car to the new EU states. And that means you're not insured there, and the border guards certainly look out for that.
You HAVE TO be insured at least third party, since car insurance is EU-wide, so I doubt anyone has ever been stopped at the border because of that. And I am guessing that the fact that the rental contract may not allow you to take the car out of countries XYZ (old EU+Switzerland or something) won't interest border police that much either.
For the record, I've crossed the Italo-Swiss border without any control but was asked for travel documents after a Greece-Italy ferry crossing and frowned upon when I gave'em my Greek ID card instead of the passport they were expecting to see.