What is the best airline/route SFO to Athens?

I'd suggest either SFO-LHR-ATH via Britsh Airways or SFO-FRA-ATH via United/Lufthansa.
Both have the most frequent non-stops to Europe from SFO with continuing connections to ATH.

cabovacation,
I always fly to London from SFO when going to Spain..there are two flights a day..one at 4:00 p.m and the other at 7:00 pm..I have been happy with British Airways both times..you get your own personal t.v with lots of channels too...and a nice crew. Some here hate Heathrow but I never had any problems connection through with them..however there seems to be a big problem with lost luggage there...make sure you buy travel insurance and carry as much as you can in your carryon.

Angela

How about SFO - ATL - ATH on Delta? I don't know if Business Class is an option, but I recently flew Delta's new Business Elite, which was pretty nice.

You could also travel SFO-Jfk-Athens. They are the only US airline I believe that flies nonstop from the US to Athens(either from JFK or ATL)?

Thank you all for the good ideas!

I'd suggest Delta Airlines: SFO-JFK-ATH or SFO-ATL-ATH

Continental flies EWR-ATH. But SFO-EWR will be on a narrowbody for the trans-con, and EWR isn't the best place to transit.