If you have a valid session cookie for a given user, you actually do have access to the messages in the Stack Exchange dropdown using the following URL:
http://stackexchange.com/genuwine
This URL returns the user's most recent notifications across the network as JSON data.
Keep in mind that this would only be useful in a situation where you have access to a user's session cookie - such as in a browser extension or addon. Apparently there is reason to hope that this will eventually be implementedthere is reason to hope that this will eventually be implemented when the next version of the API rolls out.