Europe differs a lot from country to country. Some countries have very high unemployment rates, others (such as Norway) suffer from systemic under-employment, and generally imports workers.
Before I sold my start-up, I hired employees from many different countries, and with the exception of one coming in from Russia, never had problems with immigration papers, etc. (We eventually got the Russian in, but it took a bit of time and hassle. It was worth it, he was great.)
So, can you do it? Sure.
Now, how to do it. Looking on job boards is a good idea. Prepare a good CV in English (have a native English speaker proof-read it). Be prepared to sell yourself in a cover letter. You want to seem eager, but not desperate.
Be ready to prove your chops. Have good recommendations, code samples, contributions to open source projects, what-have-you. You need to be able to demonstrate that you are worth the bother.
If you have enough savings, and have decided on a country you want to live in, self-finance a trip to visit. Let prospective employers know you are coming. Even if you don't get a bite during the visit, having been to the country will make you look more serious to other employment prospects from that country down the road.
Finally: see if any employers in your home country also have branches in the places you want to work. They might be able to help you out.
Good luck!