Jeff pretty much covers it.
In speakers, the one thing which will wear out in about 10-15 years time is if you have a woofer which uses foam surround. This will get dry and crack over time, especially in a smoggy/smoky/damp environment. However there are companies which sell re-foaming kits for various models. Its a bit of a messy process, but I've replaced the foam multiple times and the resulting speaker is as good as new, for another 15 years (my 18" JBL subwoofers and the woofers in my JBL 4412 monitors use foam). If you have the same speakers over multiple decades (like 40-50 years) and they use ferrite magnets, a re-charging might be a good idea if you really value the speakers. The difference a re-charging will make is not dramatic, but again, if you are picky and really value the speakers, I'd take them to a speaker repair facility and have this done. Speakers which use Alnico magnets, which are of extremely high quality but not used these days because of cost, do not really need to be re-charged unless you are really picky (I've done this to my Altec woofers and compression drivers, just because I could).
In turntables, if you keep the main bearing oiled, it will last forever. If your turntable uses a belt, I'd buy a replacement while you can and use it if the original gets too stretched out. The belt on my Thorens has been replaced once; I bought this turntable in 1972 and it still works as if new.
Traditional analog components don't really wear out with the exception of electrolytic capacitors which may dry out. If you've had an amplifier, preamp or similar for more than 30 years, I'd have the electrolytic capacitors checked. Big electrolytics can short out and spew their guts through their vent hole, and smaller ones can stop acting like a capacitor. Ironically, vacuum tube electronics seem to stand the perils of time better than solid state electronics. The pair of Dynaco MKIII tube amps I built as a kit in 1968 have functioned flawlessly since - and I still use them almost daily. I have some gear from the 1950s, and have never had a single problem with any of it, and it still gets used. My big vacuum tube tape recorder was built in 1962 - it still works like new.
Electromechanical components like pots and switches can deteriorate if the gear is in a smoky/smoggy/damp room. The #1 killer of these components (and humans themselves) is smoking. Don't do it! Contrary to popular thinking, squirting "cleaner" into pots will not give a permanent fix. It may clear up the problem for a couple weeks, but the noise will come back. Frequently the problem is a leaky coupling capacitor upstream of the pot which is letting DC voltage get to the resistance material on the pot. Pots should never have DC voltage on them, period. Contact cleaner on switches is more likely to fix a problem, but there is technique to it, which I don't have time or space to go into.
If a transistor or IC fails on older solid state gear, there might be little chance of finding an exact replacement. YMMV. Contemporary digital gear is FAR WORSE! This stuff is not designed to be "fixed" at all; if it fails, all you can generally do is throw it in the trash.
Realistically though, none of the above matters since there are so, so few people who keep "old" sound gear in the first place. Just buy the latest stuff and throw it away when it breaks (recycle it if you must, YMMV).
