I am looking for an online booking engine for discount flights inside Europe. Does it exist ? If not - what is the best strategy to shop for intera-European flights ?

Not for booking, but to shop, see www.whichbudget.com or skyscanner.net - - for the low cost options, at least.

Perhaps see also www.opodo.co.uk - - though i find that cheaper fares may exist on the routes they find for you, on the airlines own web site.

Best wishes,

Rex

whichbudget.com is a good start.
Since I found whichbudget not necessarily 100% up to date with the current situation (low cost carriers abandon or start new routes often more frequently than signature airlines), I usually also check the airport's website from where I want to depart.

Make sure you know which airports these airlines connect, i.e. Barcelona or Barcelona-Girona with Brussels or Brussels-Charleroi. Going to secondary airports usually takes a bigger chunk out of your time when additional time-consuming transfer (calculate costs) is needed to get to your destination. Yet it can be worth while when you get a good deal.

www.swoodoo.de

try www.airninja.com

Goo point, always check out airports and how to get to them, some cheapo airlines have flights that leave at 6 in the morning, which is before public transport can get you to them, so often meaning an expenisive taxi or a night at the airport.. example, for Paris there are three airports, two are fine, but one, Beauvais is about 100 km from city.

The normal booking engines will also do intra-Europe flights - they aren't just for flights involving the US.

www.travelocity.co.uk and www.expedia.co.uk. These are not the same sites as the US ones.