I've found that the majority of faults come down to:
Faulty mains filter or DC output filter capacitors, Shorted output rectification diodes, Shorted switching transistor, Failed fusable resistors
... with the exception of capacitors that have gone high-ESR (rather than visibly bulging/leaking), you can check for those with a simple meter.
Sometimes you do get a cascade of faults (I remember one lovely fault in a Sun PSU which blew half the components and burnt many PCB traces), or the faults aren't cut and dried (e.g. I had a PSU in an Acorn machine where the 5V rectifier would only die when under heavy load), but the above does seem to take care of the vast majority of problems and are pretty easy to check for even without a schematic.
cheers
Jules