Recapping

If its on Fire !

In reality unless you experience a catastrophic visual or audible failure the nature of aging capacitors, in the main Electrolytic or say vintage paper in oils, means that drift from spec will tend to progress over time meaning that you may not really notice as you acclimatise to the sound over that period of time,,, A good multimeter is your friend...

@doogiehowser makes some good points

After recapping and a few other things of a few vintage items I find the difference can be big depending on the type of caps and how old they are.
one example is My Sansui CA-2000 Pre amp. before the restoration it worked fine the sound was warm, full, 3d and a little rolled off typical of what many say vintage sounds like. After the restore the overly warm sound was now neutral, better bass extension and detail, much bigger 3d sound stage and the detail level increased substantially specifically the decay of notes. I feel it went from an ok typical vintage piece to a very nice modern sounding preamp.

I highly recommend a restore on 30-35+ year vintage items. Also recommend replacing the older style speaker binding posts and RCA connectors more for convenience and reliability then sound.

of course this depends on what the vintage item is but I think anything old can benefit from a restore.

I do not follow the "if it ant broke don't touch it" mentality that's just asking for trouble....would you get on an airplane if the company's maintenance policy was don't fix it until its broken? 

Leakers.

          What glennewdick said: +1

                  Any/all electrolytics!

The symptoms I experienced with my vintage Mac SS were low hissing in the affected channel and loss of volume.

Capacitor degrade badly over the years, on/off cycles, heat, overvoltage all affect the life of a capacitor, the older they get the ESR increase and the capacitance decrease eventually. In addition to the power supply electrolytics replace capacitors where there is a heat source, big hot transistors, valves. Also paper in oil coupling caps may leak over time so I would replace them too.