Companies like Busabout , Eurolines and others offer flexible passes, like Eurail, at up to a third less than the train. All these tickets can be arranged beforehand. Paperwork, insurance, rental or purchase costs and fuel will add up quickly. You will need an International Drivers Licence, which you can obtain from some travel agencies and your local motoring society. Driving rules vary from country to country, and roads can be very busy at peak hours and during holidays.
Most highways also charge tolls, France is notorious for highway tolls.
If this does not put you off, driving Europe will let you discover out of the way places and sights that only locals know. Flights are becoming a budget option in Europe. Check out great deals from low-cost airlines like Virgin Express, Ryan Air and others. Passes are also availalble from groups like Europe by Air. Hitching is not recommended on safety alone.