I'm just "filling a small gap" to the correct answers provided by irishguy28: Assuming that you are flying into ATH from a non-Schengen country and that your connection is a "real" one (a few hours that you can easily spend in the non-Schengen part of ATH and not a real stop-over as mentioned in the title of your thread), you will not need a visa. Otherwise, i.e. you do leave the non-Schengen area in Athens, you will need a regular visa. Needless to say that, if coming from a Schengen country, the visa used to enter that country will still be valid for Greece.