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, Twitte
There is a non-depreciated equivalent to the twitter or sharer.php functionality, though it is way more annoying. This doesn't exactly answer the question about "liking" a page but does accomplish the exact analogy to the twitter share, which seems to be what the question is asking.
Now make your url like this:
http://www.facebook.com/dialog/feed?app_id=000000000000000&link=http://example.com/whatever&redirect_uri=http://example.com/backtothesite
You would think the redirect_uri would default to the user's facebook home or to the link parameter, but it's a required field.
More parameters here: http://developers.facebook.com/docs/reference/dialogs/feed/