I had my bags searched on a train Europe, in the middle of the ride, not at a crossing. Just taken out and rifled through. Say what you will about the States, but that's unconstitutional here --- except at the border.
Obviously it depends where in Europe you are, but in the UK at least, the police need reasonable suspicion before they can search you (or certain other specific circumstances must obtain), and there are limits on what they are allowed to search for. They are not legally allowed to search you just because they feel like it.
There's a summary of police powers of search and seizure in the UK here:
