What is being PUT (in the verb sense) onto the server if there's no content? The spec refers to the content as "the enclosed entity", but a request with no content would have no enclosed entity, and therefore nothing to put on the server.
Unless, of course, you wanted to PUT nothing onto the server, in which case you'd probably want a DELETE instead.
HTTP requests have a body if they have a Content-Length or Transfer-Encoding header (RFC 2616 4.3). If the request has neither, it has no body, and your server should treat it as such.
That said it is unusual for a PUT request to have no body, and so if I were designing a client that really wanted to send an empty body, I'd pass Content-Length: 0. Indeed, depending on one's reading of the POST and PUT method definitions (RFC 2616 9.5, 9.6) one might argue that the body is implied to be required - but a reasonable way to handle no body would be to assume a zero-length body.
A body is not required by the IETF standard, though the content-length should be 0 if there's no body. Use the method that's appropriate for what you're doing. If you were to put it into code, given