"Way back when", disk drives were the most frequent point of failure. They had expected lifetimes equivalent to a few years of continuous operation. For today's hard drives, the expected lifetimes are on the order of 20-40 years.
Floppy drives are prone to go 'out of alignment' after a number of years. This matters *only* if you are using floppies to transfer stuff _between_ different machines. An out-of-alignment drive can read material written on _that_ drive w/o problems, although trying to read those disks on a different machine, or reading disks from a different machine _on_ the out- of-alignment drive, results in 'data error' failure messages. How long it takes a drive to go out of alignment depends on the quality of the drive construction, and the physical abuse that the system containing it is subjected to. It's usually _much_ cheaper to replace the drive, than pay for the labor to have it 're-aligned'.
The 'electronics', assuming they make it past the 'infant mortality' stage (the first 100 hours or so, of operation) are easily good for 20 years, and probably _much_ more.
If they can't do it themselves, they _pay_ somebody to do it.
There are software tools that let you transfer via a serial port, or parallel port, or even USB or Firewire, between two computers.
Drive 'compatibility' is pretty much a "non-issue". *Very* old PCs used, primarily, what were called MFM drives, Or sometimes a cousin thereof, called RLL. Newer generations -- meaning most 386/486 class machines, and everything past that -- use what is called IDE. IDE has gone through a number of changes, adding higher-performance options to the base technology.
You cannot use a MFM or RLL drive in a machine that has support only for IDE drives. HOWEVER, the earliest IDE drive _will_ work in the most modern IDE machine. And, if one is sufficiently determined to use the 'antique' drive, it is usually possible to drop an appropriate 'controller' card into the newer machine to run it -- this approach may not be viable if you have a machine with *only* PCI expansion slots.
Then there is the issue of any software installed on the old drive. If that drive was in a machine running a MS operating system that includes the "Registry", most software will _not_ be usable if the disk is simply installed in a new machine, nor if the software is 'copied' from the old machine to the new one. Because the required "Registry" settings are not propagated to the Registry on the new system. General practice is to 'reinstall software from the original distribution media', then copy any _data_ files over. It's a real time-waster, but Microsoft doesn't think user's time has any value. *snarl*
I've got _twenty-year-old_ PC equipment that's still running today. One example being a "TI Business PRO 286" box. I still use it because I haven't found anything that can replace it, at an affordable price. Notably because it has *fourteen*(!!) usable expansion slots in it. And I've got them _all_ full with various specialized goodies. It would take at least 3 'semi-modern' machines to provide the same number of 'usable' expansion slots.
Well, maybe not. I just saw an ad for an odds-and-ends dealer, that has a 14 slot rack-mount box, with a 486 processor card, for about $300. That's a *LOT* of money for a 486 box, though.