DOSBox

WHERE TO FIND GAMES:
Good place(s) for downloading MS-DOS games:

- Myabandonware
Has many DOS games for download. Easy to use and you will find all common games there.

- Archive.org
Many directly playable games via the build in DOSBox emulator. If you want to play the games in a browser this is a good starting place. Download is also possible.

- Total DOS Collection at Archive.org
TDC is the biggest archive and collection of DOS games. If you can't find a game on the other sites its worth to check out TDC.



Emulation:
DOSBox is the emulator of choice to run DOS games and applications on modern systems (there are no DOS drivers for modern hardware devices). The community develops different DOSBox builds all the time. If the official standard is missing a feature there might be builds that have it.


Versions:
Since all versions of pure DOS (not including the DOS versions bundled with Windows operating systems) are fully(?) backwards compatible (except MS 4.0), there's no reason to identify the versions any more specifically than blindly assume all games run on DOS 5.0 - the last real DOS (6.x added disk compression and after that the features were being stripped).

MS-DOS 4.0 was not the next step after MS-DOS 3.3. 4.0 was instead an update to MS-DOS 2.0 that added multitasking. It widely broke compatibility and caused regular freeze ups. Microsoft quickly replaced it with 4.01 that helped but did not eliminate the issues. IBM wisely chose not to base its PC-DOS 4 on MS-DOS 4.0 and instead updated 3.3 to create PC-DOS 4.00. When MS-DOS 4.0 became infamous, IBM made a very minor update to their PC-DOS 4.00 and released PC-DOS 4.01. PC-DOS 4.00 and 4.01 are indeed different from MS-DOS bearing the same version numbers. MS-DOS 4.0 was so infamous that makers of DOS clones did not use "4.0" as their version number. Digital Research skipped to "DR-DOS 5.0" (later causing their MS-DOS 5.0 clone to be labeled "6.0"). Novell DOS also skipped "4.0" and followed the same pattern as Digital Research. Since many customers chose to downgrade to MS-DOS 3.3, Digital Research also improved their DR-DOS 3.3 clone and labeled it DR-DOS 3.41. Even Microsoft president Jon Shirley later said, "maybe we shouldn't have called it DOS 4.0".

So, if a game lists "MS-DOS 4.0" in its system requirements, that it is certainly significant.


IBM PC-DOS 2000 (Not by Microsoft) was the last official DOS. It included the features of all previous version plus a few more and Y2K compliance. It did not include any of the problematic features (or lack thereof) of MS-DOS 7.x or 8.0. No games are known to have been written specifically for 2000.