Am I crazy or is it possible to travel from Paris to Athens by rail and, if so, how? Has anyone done this?

Yes, crazy would be the correct term. I entered the cities on the German rail site and the trip time was 47 hours.

It is a long and uncomfortable train journey, but it is a very pleasant journey by train and ferry via Italy. For example, take an overnight sleeper from Paris to Venezia, then a ship to Greece (www.minoan.gr or www.anek.gr) or take the sleeper to Bologna, then a train to Ancona for ships to Greece (www.superfast.com, www.minoan.gr or www.anek.gr). The ships have cabins, restaurants, sun decks, etc. You arrive in Patra, then continue to Athens by train or bus.

It is possible as Geoff has said; has also been done via Brindisi; IMO it is not crazy. It would be memorable for you so why not do it?

In terms of a trip purely by rail, the SNCF site says "not sold on this site because more than 3 transfers required."

See www.seat61.com/Greece.htm on "how to do it" - just ignore the bit about "London to Paris by Eurostar"

I love the guy in Seat61...very helpful.

here's yet another variation on the route..
Paris via Zurich and Beograd to Thessoloniki to Athens..eliminates the ferry ride altogether.

If only I had the time to do it....

"eliminates the ferry ride altogether."
Why would you want to eliminate the best part of the journey? There are trains which will take you all the way to Greece via Serbia, but the problem is that their facilities are limited. The ships between Italy and Greece have cabins with bathrooms, restaurants, bars, lounges, etc. The train journey only makes sense if you can break the journey by spending a day or two in places en route. I'm a great fan of international rail travel, but not for spending 48 hours on trains without a break.