1. A machine-implemented method for providing an Internet fax service, comprising: (a) receiving messages through fax transmissions on a plurality of direct inward dialing (DID) lines assigned to a plurality of users of the service, respectively, and storing raw fax documents derived from the received fax transmissions, respectively; (b) retrieving the users' account information to determine each of the users' subscriber status or subscriber classification including whether or not the user is subscribed to the Internet service; (c) making the received messages available to the users, respectively, over an Internet and in accordance with the users' account information; (d) performing the following on a per user basis according to the user's subscriber status or classification, (i) processing the raw fax documents using digital character recognition to extract text therefrom, (ii) scanning the extracted text to find one or more specified keywords therein, wherein the found keywords are a subset of the extracted text, (iii) storing the found keywords in association with their raw fax documents in a database; (e) receiving a plurality of requests for message searches, from two or more of said plurality of users, respectively, in accordance with each user's account information; (f) processing each one of the plurality of requests by searching amongst the found keywords that are stored in the database to find ones that satisfy search criteria designated by each one of the plurality of requests; and (g) making results of the searching available over the Internet to said two or more of the plurality of users, respectively, in accordance with each user's account information.
2. The method of claim 1 further comprising: prioritizing one or more of the (i) processing, (ii) scanning and (iii) storing, depending upon subscriber status or subscriber classification.