I just tried to play Morrowind and when I loaded my game, in the middle of "Initializing Data" it stopped loading and a box popped up and asked if I wanted to continue to run executables, yes, no, yes to all?

WTF? This never happened before, so I said no, and the game closed. So I tried a different save and a different save and got the same thing and then when I went back to my fourth newest save, it loaded without stopping at that point.

What the hell is going on? Does this mean my three newest saves are somehow corrupted? I have NOT added, changed, deleted, or touched the setup (i.e. mods, mod options, game options) in any way.

What the heck would cause this? If I go back to that fourth newest save and lose those hours, how do I know the same thing won't happen again when I save the next time?

I don't understand this at all, but it could mean the end of my Morrowind experience this time, and that would be a shame because I'm having fun.

I guess you activated or de-activated a mod. The box also tells you what file it's complaining about, which might give you a hint where the issue is.
You can also try to ignore the messages (say "yes" to "continue to run?") - very often it doesn't break the game (for example, it might affect a texture or a game area you may never reach), and it's not going to damage the Morrowind installation or the save files. To be on the safe side, I wouldn't overwrite the save files you want to keep, use a different one for future saves.
But you're better off trying to find out what the game complains about, and either fix the issue or make a deliberate choice whether or not you take the risk to continue without resolving the problem. If you do, the message(s) will pop up again whenever you launch the game.
If you start a new game, this will not have the issue.

I am absolutely positive I didn't activate or deactivate any mod. I haven't touched any such settings since the beginning because I had such a hard time getting it installed just right.

The real time between the fourth newest save (which loads fine) and the third newest save (none of the first three newest saves load without that popup) is eight minutes. Eight minutes. I was simply playing the game and saved it 8 minutes later. No changes to mods.options, settings, nothing.

And the only thing that appears in that pop up box is an O or a 0. That's it. I'm pretty sure there is no esm or plug in named O or 0. But that's all that appears in the pop-up box.

It's very confusing. And disheartening. I'm going to start again from that fourth newest save, play about 8 minutes again, and save it again and see what happens. Of course, I have no hope of repeating exactly what I did in those minutes since I can't remember exactly, but I did go ahead and click yes to all on that third newest save to get a look at my character and I have an idea of some of what i did in between.

Are you using the Morrowind Code Patch (MCP) ?

In particular this component:

https://staticdelivery.nexusmods.com/mods/100/images/19510-1-1272382529.jpg

It will not fix your current problem, but it will decrease greatly the chance of it happening again.

Yeah, I am, and yeah, I'm pretty sure that's one of the "default" checked items when you install it. So it should be installed.

I'm not sure it's a corrupted save. It may have been something I did in game, which is actually more troublesome to me. I was saving over games, but since this occurred I've been creating a new save every time. But if it was something I had done in game, it makes wonder what action caused and what possible other actions in game might cause such a thing. Guess I won't worry about it unless it happens again. If it happens again, despite running that save game corruption patch AND creating a new save every time, then it might certainly be something that is happening in game.