If you need to fly as part of your European trip to cover a large distance quickly then you might want to try the following airlines in Europe, they offer cheap flights and deals which can be comparable to the cost of a train fare, just make sure you factor in all of the costs.
European Budget Airlines:
Air Berlin (German)
www.airberlin.com
Blue Air (Romanian)
www.blueairweb.com
easyJet (British)
www.easyjet.com
Fly Niki (German)
www.flyniki.com
GermanWings (German!)
www.germanwings.com
Jet2 (British)
www.jet2.com
Norwegian Air Shuttle (Norwegian!)
www.norwegian.com
Ryanair (Irish)
www.ryanair.com
Smart Wings (Czech)
www.smartwings.com
Transavia (Dutch)
www.transavia.com
TUIfly (German)
www.tuifly.com
Vueling (Spanish)
www.vueling.com
Wizz Air (Hungarian)
wizzair.com
We'd also recommend searching on SkyScanner to make sure you're getting the cheapest available deals.