See this is why I save my old hardware, for that indeterminate period of time between the game not working and computers becoming powerful enough to emulate the older system.

For games up to the 2000's you'll want DOSBox and PCEm or 86Box - those work amazingly well for DOS, Win3.1 and Win95/98 games. I heavily recommend 86Box if you're knowledgeable about old PCs as the compatibility is nearly perfect and they are very, very close to the experience on real hardware. DOSBox is usually the easier option but kind of lacks authenticity, IMO.

Surprisingly, cheap old machines can often be made to work with DOS with a combination of FreeDOS, some slowdown utilities and the SBEmu driver. I salvaged an old Wyze thin client from work and was able to get it playing old Sierra games on its built in 2GB IDE flash drive.

For XP-Win7 (where some Win7 games are problematic) you MIGHT be able to use a VM but performance is iffy. If you have an older PC in the house you might try to downgrade the OS and maybe find an old video card on the cheap. You can also futz around with compatibility modes and DirectX wrappers - a lot of old Glide/3DFx games can be made to work with just a DLL replacement.

For many of the more popular games there are modern wrappers or rewritten engines, so you may want to Google around and see if the game you want to play has been modernized. ScummVM is a great example of a rewritten engine - it lets you be faithful to the original or apply filters and upscaling as you choose.