I have a couple thousand core.* (where * is a number) files in my user's home directory. They are taking up a ton of space, and I'm not sure where they came from or how to find out. Can I delete them or what?

Are using using KDE? I just remembered I think I've had them before but I don't remember when. I haven't used KDE for aaaaggggeeeessss so it could be just Konqueror dunping session data on an unexpected exit or something. I'd delete them, my system is running fine without any /home/cam/core.* files

core* files are core dumps. Whenever a process exits with a special return code (on a system error, for instance), the "core gets dumped". This means that the main info you need, like the stack of the process that failed, gets written to a file.

Normally, by looking at the contents of the core* file, you should be able to determine what went wrong and you should be able to debug the program.
However, in most cases:
-the core* files are really big
-the core dumps are not caused by any of the programs you've written, but from other people's apps. In this case, you may not be able to debug the program, even if you wanted to.

So, in general, most people just throw away the core* files. If you want to supply a bug report to the developers of the app that cause the error, you may want to think about keeping the core* file around so that those developers can take a look at what went wrong.

If you don't want to submit a bug report or if you don't know what app halted unappropriately and dumped the core, you can safely remove the core* files to free the disk space.

If you however get new core* files regularly, then one of your apps may be broken. In this case, further investigations or a re-install of the app in question may be needed.

IOW, do any of your apps crash regularily or frequently?

I will delete them, thanks. I've had errors, but I've had so many I don't know what's from what.

About a couple thousand, I'd imagine.