In addition to replacing the large power supply filter capacitors, many people who refurbish old receivers or amplifiers will upgrade/replace the coupling capacitors in the amplifier circuit. These caps can become defective and cause one or both channels to sound scratchy or distorted.
Generally its only electrolytic capacitors that need replacing, the most critical being the ones serving as filters in the power supply. Occasionally resistors that are stressed (like ones near the power tubes) can fail, and in some designs its a good idea to replace some of these with higher tolerance ones before they fail.
I have power amplifiers which have capacitors which are over 30 years old and still good. These capacitors don't degrade the sound in some mystical "audiophile" sense, rather, when they go bad, they lose their ability to act as a capacitor and audible hum is the result from inadequately filtered DC in the power supply.
Another option to consider when replacing electrolytic capacitors in your gear is to purchase modern axial capacitors with high voltage ratings. Axial caps in particular are useful in power supplies constructed on turret boards, common on vintage guitar amps.
For electrolytic caps (and really all caps), there are testers that check "equivalent series resistance" (ESR), and leakage (or dielectric strength). Then it becomes a pretty clear result of pass/fail instead of "replace on general principle". ... Other than capacitors what parts within an amp need replacing because of age?
Electrolytic capacitors are really the only ones which degrade over time, and in a power amp generally last over 10 years, sometimes much longer than that. I have power amplifiers which have capacitors which are over 30 years old and still good.