Brent, this is a really interesting question. I do occasionally "Like" my own posts, especially if I think they will generate a good conversation.
Why? Because then I get updates on all future comments on that post. For now, Facebook does not offer the ability for Page managers to automatically follow comments on their Page (at least without some paid third-party tools). However, if I leave a comment or "Like" the post, then I'm notified of future comments. So I do it more to monitor the ensuing conversation that to be self-promoting.
If anyone has a better way to monitor posts on your Page, I'm all ears.