Turkish Airlines are good value and good service, newish planes, too. Direct to Istanbul from Dubai, then hope for a not too long wait for transfer to Athens, for example. Of course, there's always Olympic, but they only fly out of Abu Dhabi!
P.S. Sorry, internal airlines, of course Olympic, also - darn, can't remember the name of the good one, will ask husbad when he returns later (Greek, in aviation). Why not take ferries from Athens once you're in Greece, though? Good fun and relaxing.
<em>edited by simpleasabc on 08/01/2011</em>
Turkish airways is another one to look at as well, is my hubby's fav 'new' airline for europe. You go through Istanbul, of course, and then just about everywhere else for next to nothing. If Fly Dubai or air arabia can get you there, worth looking at too, as they are neat little budget carriers.