A close friend and I are thinking about spending a year living and working in Europe. I'm interested to learn about any potential opportunities that would allow for travel around Europe and would provide enough $$ to off set the traveling expenses along the way.
I know of quite a few English speaking people who have set up a base in the United Kingdom doing bar work etc - not always great wages I'll be honest but some have had accommodation as well - then travelled to the continent on days or weeks off. Travelling in Europe is very cheap compared to other places - you can fly UK to Italy from as little as £20 each way (plus taxes)! Personally, though I'm not a big fan of the UK - hence I keep leaving it ha - but I don't know how easy or hard it is for non-EU people to get a job on the continent particularly if you don't have the language. Another option is www.workaway.info. You get food and accommodation in return for a few hours work and some of the projects they have are so interesting you would pay to do them! You can move between projects spending days or weeks at each and visiting a few places in between and it would cost you very little overall if you planned it well. You might even want to couch surf on your days off to save more money.
Hope this helps a little :)
Teaching English is an option, especially in Eastern Europe. I recently completed my TESOL (Teaching English as a Second Language) certificate here in Prague, and am now teaching here and traveling around Europe when I can! A TESOL certification, if you get a good one, can also enable you to teach all over the world.
Agree with Emily! Workaway.info is great! I managed to travel around South America so cheaply using that website. Also I got a TEFL before I went and took on some teaching jobs. Take a look at my website that has loads of advice on how to travel cheaply http://www.coffeewithasliceoflife.com/2014/03/03/how-to-get-a-tefl-qualification-on-the-cheap/