Something that has come up is that there's apparently some forks of DOSBox that may offer features that are not in the main version. (I've heard of save states in some fork, for example.) Does anyone have a rundown of the various DOSBox forks out there?

Also, if you want, you could mention other emulators that are capable of playing DOS games. (I believe I once used bochs to play an old game, for example.)

There's a list on the DosBox page itself.
A better list is here.

An emulator that is in early development is WineVDM.
On the main page there you can find a lot of emulators for almost everything.

No need.

The only two alternatives to DOSBox 0.74-3 that really matter:

DOSBox SVN - the currently developed DOSBox version (which will eventually turn into DOSBox 0.75, a few decades from now).
DOSBox-X - integrating a lot of third-party patches and coming with a GUI as well.

If you want to emulate something more complex than DOS, you should explore the PCem/86Box route. Everything else is superfluous, right now.

And what about
DosBox Staging, which aims to drag DosBOX kicking and screaming into the modern age, with a modern development pipeline and modern technologies, having made progress on what were previously classed as headbangers of problems, such as not being able to accurately play the WizzBall intro?

*deleted*

One such feature is GUI, but there are some frontends which attempt to provide that.
It is a bit unfortunate that there's no official thing for that, something like ScummVM interface. That list would be very long, because there are many game-specific applications to run older games in modern environments. Technically speaking most of them are not actually emulators though.
The last one I used was a patch that makes the original Tomb Raider a Windows game, kind of.

ScummVM probably has the best compatibility list of games, but again, it's not really an emulator.

If you can find an OS/2 emulator somewhere, that might run a good number of DOS games.

To narrow the field down a little, I'm interested in actual emulators, those that can emulate something like an x86 PC running (some version of) DOS. In other words, I'm not interested in things like ScummVM or other engine re-implementations here.

For example, suppose I want to make a tool-assisted speedrun (TAS) of a DOS game. What emulator would be suitable for that?

The best one seems to be JPC-rr (java):

https://tasvideos.org/EmulatorResources/JPC

Here's a fun one with my favourite; Captain Comic
https://archive.org/details/comic-livetas-20201009

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We can both disagree over the choice of host, but I do think git is far less byzantine and inelegant than svn.
Sure, the project could be hosted on Gitlab, but that's a problem for them.

Git is known by more developers, I won’t deny that (they still mostly misuse it, but this is another topic). But starting a fork based on a VCS choice, especially now that we have tools allowing us to interact with an svn repo like it were a git one, does not sound like a serious basis.

By the way, I see the GitHub → GitLab.com recent migration as being a same symptom of common developer stupidity than the previous SourceForge → GitHub one, or for IRC users the Freenode → Libera one. When will they actually learn anything?!

Shrug. A lot of these people are the same type who claim that cryptocurrency is the ultimate in decentralized currency, while relying on centralized services that can, and often have slammed shut on their faces.

I don't think the freenode -> libera migration fits in the same category. Thing is, freenode had a hostile takeover, and as a result the organizations had to move to a safer space. Furthermore, freenode, as it used to exist, was shut down entirely, at which point even those uses who would have otherwise stayed were removed; the number of users dropped to *0*. (There's a lot of drama involved in this instance, including an attempted bribe of sorts.)

On the other hand, sourceforge and github still exist and are functional, with github, in particular, still being widely used.

Edit: Another thought: What happened with freenode could be compared to what's been happening with twitter lately, except on a smaller scale and in a (much?) shorter timeframe.

The ones that manage dosbox staging were banned from VOGONS right before my eyes, and I don't think they can "continue" shit :-)

At this point, they just "stole" someone's code (if stealing can be a concept in open source software) and declared all by themselves that they were doing the next big thing in emulation.

To me, dosbox staging feels exactly the same as Libretro/Retroarch: a giant load of crap with all the wrong priorities, and totally worthless - ie, superfluous - compared to their respective original projects.

I frankly don't give a flying fock about SDL2, multi-platform, touch screens and other "modern" stuff. We're trying to play DOS games here, for focks sake :-D