Here are 2 tips from The Traveling Professor on flying to Europe comfortably and inexpensively:

Make Scotland or Spain part of the flight plan:  Right now (and this can always change), two of the least expensive places to get to in Europe are Scotland (either Edinburgh or Glasgow) and Spain (Barcelona or Madrid).  Fares to these regions from sample airports like New York and Boston can be in the $500's or even $400's for a round trip flight.  In our last trip, even though our last destination was Split Croatia, we took a short flight to Barcelona to take advantage of an incredible deal in flying back to the United States on American Airlines.

Fly Premium Economy:  Flying coach can be brutal.  Tight seating, crowds, lousy meals, no storage space for bags, etc.  It really is horrible.  The "premium economy" class is a relatively good bargain.  The seats are comfortable (I could actually sleep comfortably) and there was way too much food (and good food too).   We got priority boarding, bonus miles, had access to the airline lounge.  We actually had a very bearable (and might I say, "enjoyable") flight.   Our first premium economy flight was an open-jaw New York to Edinburgh flight with a return from Barcelona.  The cost was about $950 for premium economy compared to about $650 for economy.  We also upgraded to premium economy on Air France on our flight from Paris to Split for $100 each. The Air France lounge is really nice!

Bonus Tip:  Avoid flying through LHR (London)