The longest European route is the E40. It has a length of over 5'300 miles and one can visit 13 European countries and there are even plans to build additional parts.
The highway is interesting because it leads to a lot of frustration in Western Europe because of the daily traffic jams (especially around Brussels), but in the Eastern part of Europe, it is debatable whether it is really a highway: sometimes the road looks more like a paved road with pedestrians crossing.
In the far Eastern part of Europe, one also might have some problems with corrupt police, so one must be a bit careful.
Belgian national television once made a documentary where a crew drove the entire route (stopping now and then) and visiting strange people that live near the road (again East part of Europe). You can find a small report in a newspaper here (in Dutch).