The Media History Project is a non-profit digital library of classic media periodicals. Some of the titles you can read are The Film Daily, The Hollywood Reporter, Motion Picture News and Photoplay. As well as gossip magazines you’ll also find technical publications and film studio yearbooks.
The over 200,000 scanned periodical pages in the collection are dated between 1904 and 1973. This site is fascinating for all fans of the silver screen, and well worth exploring. See the list of publications in the collection. All of these periodicals are in the public domain so you can even download them for offline viewing.