- You expose your "tag cloud" through a widget on your blog or elsewhere and you simply don't want to pollute it with sites that may just pertain to some current, short-term task. (e.g. if you saved some pointers to an item that you're in the process of buying).
- You save some sites that pertain to personal content. Presumably, you have anything truly sensitive password-protected. But that doesn't necessarily mean you want to spread the link far-and-wide. Or you may just not want to publicize an interest in a particular type of information--whether health-related or otherwise.
One of the commenters on this post suggests that an alternative to making posts public or private individually is to create separate users for public and private links. I haven't experimented enough to comment on which approach is generally easier. [UPDATE: My initial take is that having multiple user ids on del.icio.us is awkward to manage because of the way the site works. You have to do a lot of explicit logging on and off; the site leaves you logged on pretty much indefinitely from a given browser image and there seems to be no way to post a tag to a specific account other than the currently logged-in one.]