Contacts, SMS messages, that sort of thing. Some people are also really particular about all their settings and widgets and such.

I just can't imagine having to worry about this.

It is why I like a low end Samsung android. It is borderline disposable and I would never view it as more than temporary storage. Works until it breaks or I lose it then start over. In the meantime, if something is that important it mounts easy in linux and I copy over what I want to save.