I think it depends on the change. If it's a major change, I'd change the URL and/or host. If I'm removing/renaming a field or otherwise changing the structure

I think it depends on the change. If it's a major change, I'd change the URL and/or host. If I'm removing/renaming a field or otherwise changing the structure dramatically, then I think a custom mime type is appropriate. If I'm just adding a field (in the case of a JSON/XML object), then I probably wouldn't bother doing anything.