For The Metal Age, Jean-Pierre Jeunet's film "La cité des enfants perdus" (The city of lost children) was a big inspiration. See the film and you'll see what i mean. (And this was confirmed by one of the devs)

As has been mentioned before, and as many know, but not all, here are the shared influences:
For TDP, the cover image of Caleb Carr's The Alienist--leading to the juxtaposition of a Dickensian poverty and Baroque ostentatiousness--Jack Vance's Dying Earth series, as well as Fritz Leiber's Fafhrd and the Gray Mouser adventures, and the movie Blade Runner were heavy influences.
Thief Gold derived much from The Phantom of the Opera, and slips in a variation of the name The Cook, the Thief, His Wife & Her Lover.

For TMA, Fritz Lang's M and Metropolis, Charles Dickens' Oliver Twist and A Tale of Two Cities, the works of Lewis Carroll, The Third Man, the works of Jules Verne, level design in the original Rainbow Six, the original black & white Beauty and the Beast, The City of Lost Children, and Time Bandits is an unofficial influence, or just Terry Gilliam's work in general (Monty Python, too). --[The fans have noted a lot of similarity between Karras and Hitler and the Mechanists and Nazis, and there's a Viktrola in Wieldstrom that sounds very much like Karras and throng of shouting followers.]

TDS was influenced by The City of Lost Children. The Cradle influences include Randy Smith's horror Thief levels, Eric Brosius's soundwork, the Silent Hill series, the System Shock series, the movie Jacob's Ladder and also Ringu, The Changeling, and other influences pending.