If you’re traveling in a group, renting a car can be an affordable and fun way to travel around. Prices vary and can be anywhere from $40-$200 a day. However, you also need to factor in gas and tolls, which can be quite substantial as gas can be upwards of €5.50 a gallon.
Also note that you might have to be 21 or 25 to rent a car, depending on the company.
If you do decide to rent a car, remember to shop around and find a plan that fits with your itinerary and budget.
Another option for getting around is a rideshare. There a number of resources to match up people looking for rides with people who are driving and have extra space in their cars. This can be an exciting and cheap way to meet some new people in Europe and travel cheaply.
Carpooling.co.uk is an English off-shoot of an extremely popular German ride sharing site, and is the largest carpool/rideshare site.
There are also a number of groups on Couchsurfing, who arrange rides across Europe and elsewhere.
Another way to travel cheap is to hitchhike. I can be a great way to travel on the cheap and get to know the local people. Though sort of a dying art, this is still rather popular among students in Europe. One of my roommates in Germany used to swear by it and would hitch all over Western Europe.
That being said, this probably isn’t for the average backpacker. While Europe is generally safe, hitch hiking does have some risks associated with it, especially for solo and female travelers. As always, use common sense and stay safe.
Backpackers Ultimate Guide has decent write up on hitching in Europe.
WikiTravel has a number of tips and strategies for hitch hiking.