Depends on where in Europe you will be and where specifically you want to fly. There are plenty of budget airline routes. EasyJet, Air Berlin, Ryan Air etc. There will be also local carriers.

An ok site to use to search for flights is
http://www.skyscanner.net

Also depending on how much time you have I would recommend checking out long distance buses or inter europe rail services. So you could fly up to Tallin in Estonia and catch a train/bus to St Petersburg. Plus ferries run between Southern Spain and Morroco etc

So check out http://www.eurolines.com and a good website to check cross Europe rail schedules is http://www.bahn.de