Well there are some guys at a local airfield going for this very record doing rather large circuits in a C152!
Yes, but it is not scheduled - I think.
Some folks flew something like 2 months without landing - back in 1950-s or 1960-s or so, on small GA planes. They refueled in air - by hose from trucks running on road beneath.
However, among the scheduled services the A340-500 jets still do not match the flight times of Constellations back in 1950-s. Europe to western North America, nonstop (and no aerial refueling) for over 22 hours.
And THAT did not match the Catalina services between Perth and Ceylon. Nonstop (again no refueling) for 29 hours.