A quick disclaimer: No one is endorsing these airlines. Fly them at your own risk. Do your own airfare search and you'll probably find others that are as good or better. The prices listed here are examples of what was found in a single search, and you can expect your results to vary quite a bit. Routes could be more expensive and taxes/fees usually are not included.
Euroflights.com is a handy tool that matches budget airlines with European destinations. In a few clicks, you can have the budget options for your trip, with links to the actual airfare sites included.
BMI Baby Airlines bills itself as the "airline with tiny fares." It has routes across Europe, and offers specials such as a £25($38 USD) flight from its Birmingham (England) hub to Rome, or £30 ($60) to Lisbon.
Brussels Air recently offered a 55 EUR ($75 USD) one-way flight from Brussels to Copenhagen, among other deals. The site shows you daily pricing so you can shape an itinerary to take advantage of the best deals.
Easy Jet offers 188 routes between 55 European cities. They charge you a fee for booking with a credit card, and they do not issue refunds except in cases such as the death of a family member.
Germania offers a variety of discount flights between its name sake and Spain, Italy, or Greece. They recently offered Paris-Vienna roundtrip for 94 EUR ($129 USD).
Wizz Air started flying in 2003. It flies as far east as Warsaw and as far south as Athens. Its connection to Copenhagen involves a motorcoach ride from Malmo airport. Random sample one-way fare: London-Gdansk for £7.55 GBP ($13.97 USD).