First you have to enable the changing of the content type. Then you can make the
"Title" field optional and hide it.

Okay, that is good, but how do I replace it with one of my own columns?

I'm not sure what you mean. You want one of your own fields to replace the Title
field? I would imagine that would be done in the change content type area. Not
sure though off the top of my head.

Well, I have a different column, a sort of GUID, that has a "required data"
attribute set to allow only numbers. I want all the list to updated according
to this item instead of "Title". I want to use this GUID as the "title" for
email alerts, and the "title" used for the "edit item" pages.

Maybe this is clearer: If I go to list settings/List Content Type, I see that
"Item" has the "source" of "Title". I want to change the "source" of "Item" from
"Title" to my GUID column, instead.

See my other message. You can’t replace the Title column with a different
column.

I did see that you said that. I didn't know if this was
the same thing or not. Anyway, I ended up renaming the columns, calling "Title"
by the name of "GUID", exporting the list to an Access table, opening the list
with Access, sorting the list, then copying the column from my copied table into
the sharepoint list table. That works, except that I lose the "numbers only"
attribute of the GUID column. But now it is at least used as "title".

You can change whether the Title column is displayed or not, but you can't
change its use in alert emails or as the title of the edit panel. That's
all hard coded into the system and can't be changed. It can't be changed to
default to another column its too deeply ingrained into the way SharePoint
operates.

Well, since I can create Content Types, is there a way to change the "Parent
Content Type" of a list?

Yes, you can change the parent content type of a list. But that won't help,
because everything eventually inherits back to the Item content type, which
includes the Title column. As I said there is too much code built in to
SharePoint that assumes the Title column is available. Its one of the only
columns that is guaranteed to be there because it comes from the Item
content type that everything else inherits from.

Too bad they wouldn't allow a data definition for
that column!

Unfortunately there are too many constraints on how that column is used in
the User Interface and databases to be able to make that a user definable
field.

Perhaps hiding a column would work?