Is there a simple URL string that Facebook will accept to "like" a site... or more accurately (as a commenter points out below), share a site? As a comparison, Twitter allows you to post from any page simply by pointing an anchor at a customized URL... like this:
<a href="https://twitter.com/share?text=Check%20out%20this%20site:&url=http://example.com">Tweet this!</a>
I can't seem to find anything in the Facebook documentation.
Not exactly an answer, but close enough for me:
http://www.facebook.com/sharer.php?u=http://mysite.com/
That'll do it.