Generally speaking, to save energy, turn the computer off with the power button, or let it go to sleep. What stresses a modern supply is turning on and off the AC line voltage going in at the cord. That sends a surge of current into the supply under some conditions.
Leaving a low quality power supply on for years will wear out the bearings on the fan. Once the fan goes, the extra heat is what accelerates failure. This won't be a problem with quality supplies, or those used on servers. The server will go obsolete before the ball bearings on the fans wear out.
I was an engineer at a major computer manufacturer, with some involvement in specifying switching supplies, and analyzing failures.