Some of the oldest planes I have flown on were Air Canada DC-9s, British Airways 747s, and KLM 747s. The planes, however, seemed to be well cared for, and I felt entirely confident flying them.
UPS uses 1960s-vintage 727 shorties on its passenger charters; however, with their complete overhauls, new engines, and glass cockpits, they are "newer" than many of the "new" planes in other fleets.
Northern Air Cargo of Alaska has a fleet of DC-6s, and Air Atlantique has some birds of even greater vintage. Judging from the pictures I have seen, these planes appear to be beautifully maintained.
This all goes to show, an airplane that receives good care can keep on flying!
The aeroplane has unveiled for us the true face of the earth. -Antoine de Saint-Exupery