Huh?! OpenMPT does not install any components outside its own directory - none at all (in particular it does not touch msvcrt.dll, in which the crash was supposed to happen). It should not make Winamp crash in any way. The only system-wide modification that is done by OpenMPT is registering file associations. Does the problem still occour if you choose to not register OpenMPT with any file associations?
Did you get the installer from our site, or some shady 3rd party site?

Yes the problem still occurred if I chose not to register the file extensions...
And I did get the installer from your site...
Now I have a new issue. I had been running Winamp with the UMX decoder plugin and had been running this way for several months no problem. Unfortunately the last system restore point I had was before I added in this plug-in. Now when I go back and add this plug-in back in Winamp crashes. If I delete the plug-in DLL Winamp comes up just fine now even with OpenMPT installed...

I would treat this solely as a Winamp problem, but the issue did not occur until I installed OpenMPT....

Is there a chance that this is a file association problem?

I cannot imagine how file associations would cause such a problem. Seriously, it doesn't make sense, especially if you say it also happens when not registering them. By any chance, are you installing OpenMPT into a sub folder of the Winamp folder? That's the only way I could imagine them to interfere with each other, but even that is highly unlikely. I really don't think OpenMPT is to blame here. For the reference, does it also happen when installing in portable mode?

Yes it was doing it even with portable mode. That was actually the second thing I tried figuring that it might be some kind of registry conflict or something.

However, now I cannot get the problem to repeat any more and the UMX plug-in for Winamp seems permanently broken. (Winamp will start just fine so long as the plug-in DLL is not installed. Put the file in the plug-in folder and it crashes every time).

I would say go ahead and close out this bug report. The more and more I look at what is going on, the more this is looking like it is a problem specifically with Winamp and/or the UMX plug-in. Like I had said, this had been working for the last month or so and the installation of OpenMPT was the only thing I could remember doing/changing/installing in the last couple days. Perhaps it was a "Windows Update" or something else that I didn't notice happened over the weekend. Either way, I will take this problem to the Winamp forums.

Sorry for the trouble and thanks for the prompt responses.