In the US and Canada, we enjoy extremely low gas prices compared to European countries. Expect to pay up to 5 times as much for gas in many countries. In Northern Europe renting a car is an excellent idea if you can get a few people together to make it affordable. You need to hook up with a few other travelers so you can split the costs of renting the car, collision insurance, road tolls, parking and any other associated costs. And don't forget that car rental companies have a minimum age requirement for rentals.
Rental cars are prime targets for thieves.
They break into rentals knowing that, more often than not, there will be valuable items in the car. The key to avoid falling victim to an auto theft is to make your car look less like a rental car and more like one of the locals'. As well, be sure to hide all valuables in the trunk where they are out of site. Leaving your glove box open and empty also helps convince thieves that there is nothing of value in the car. For plenty of useful information on driving in Europe, check out Travlang's advice in European International Road Signs and Conventions or the Moto Europa website.