As an example, consider the two sentences:
There don't seem to be any doctors here.
There doesn't seem to be any doctors here.
To my ear, the first sounds great, and the second is painfully awkward.
So which is correct, grammatically? I've found lots of disagreement on this around the Web, with various sources citing different ways of treating the word "any" (as singular, always, or as either depending on to what it refers). No consensus, however, could I locate.