Imagine a person, tall, lean, and feline, high-shouldered, with a brow like Shakespeare and a face like Satan, a close-shaven skull, and long, magnetic eyes of the true cat-green. Invest him with all the cruel cunning of an entire Eastern race, accumulated in one giant intellect, with all the resources, if you will, of a wealthy government--which, however, already has denied all knowledge of his existence. Imagine that awful being, and you have a mental picture of Dr. Fu-Manchu, the Yellow Peril incarnate in one man.—The Mystery of Dr. Fu-Manchu (1913)
Fu Manchu has a long Evil Moustache in the famous "Fu Manchu" style.  He has squinty eyes: pure Yellow Peril. He is a Chessmaster setting up Xanatos Roulettes, and he's as much of a Karma Houdini as the codes of production allow...
His actual public domain status is complicated. The first three Fu Manchu  books were published prior to 1922 and are public domain in the USA; however, some characters are not public domain since they were introduced later, particularly his daughter Fah Lo Suee, who was only named in a later book. This has caused problems for Marvel Comics, who cannot reprint Master of Kung Fu, which uses not only Fu Manchu but other characters from the series. Also, Fu Manchu is not in public domain in Europe (Rohmer died in 1959), and Alan Moore could not name him in League of Extraordinary Gentlemen.
He has been played in over forty films by over a dozen different actors, including H. Agar Lyons (an Irishman), Warner Oland (a Swede, appearing in the page image), Boris Karloff (an Englishman, with Irish-American Myrna Loy as his daughter, here called Fah Lo), Christopher Lee (an Englishman with a bit of Italian in him), and Peter Sellers (also English) -- but never yet by an actual Asian actor, although the daughter of Lee's version was played by Tsai Chin, an actual Chinese actress. In fact Sellers' take, The Fiendish Plot Of Dr. Fu Manchu (1980), is the last movie centered around the character to date, and a parody at that.
There was also a brief television series entitled The Adventures of Dr. Fu Manchu airing in 1956. The show can be considered Fair for Its Day as it contains some sympathetic, peace-loving Asian characters as well as some villainous Western characters. However, Fu Manchu is still played by a white man (Glen Gordon) in Yellowface and it contains the same over-the-top exoticism, so it can still be a little cringe-worthy. Some episodes can be viewed here.
He probably bears direct responsibility for killing off an entire facial moustache style among the East Asian peoples of the world, a feat only matched by Adolf Hitler.
- The Mystery of Dr. Fu-Manchu (1913). A number of 1912 stories were combined into this novel.
- The Return of Dr. Fu-Manchu (1916).
- The Hand of Fu Manchu (1917).
- Daughter of Fu Manchu (1931).
- The Mask of Fu Manchu (1932).
- The Bride of Fu Manchu (1933).
- The Trail of Fu Manchu (1934).
- President Fu Manchu (1936).
- The Drums of Fu Manchu (1939).
- The Island of Fu Manchu (1940).
- The Shadow of Fu Manchu (1948).
- Re-Enter:Fu Manchu (1957).
- Emperor Fu Manchu (1959).
- The Wrath of Fu Manchu (1973). Actually a combination of the previously published stories:
- The Wrath of Fu Manchu (1952)
- The Eyes of Fu Manchu (1957)
- The Word of Fu Manchu (1958)
- The Mind of Fu Manchu (1959)
- Affably Evil: Fu Manchu
- Big Bad
- Brainwashed: Fu often uses his mental powers on his victims.
- Censorship Bureau: The production of Fu Manchu movies was halted during World War II at the request of the US State Department as China was an ally against Japan. Rohmer's publisher also voluntarily stopped publishing Fu Manchu novels during the war.
- Character Development: Fu starts out as an extreme Nationalist seeking the sovereignty of China and developes into one who seeks personal world domination. Moreover, as the series progresses Fu becomes more and more the Noble Demon type of character, a Man of Honor who occasionally even joins the heroes (as in The Island of Fu Manchu) to fight a greater evil.
- Chessmaster: Fu Manchu
- Daddy's Little Villain: Fah Lo Suee
- Death Trap: Quite a few of the novels begin with someone being murdered in a mysterious and gruesome manner (often with the victim gasping out a cryptic Dying Clue), and the hero(es) later being attacked by the cause (very often some hideous reptilian/arthropodian horror). Rohmer claimed that every method he devised was based on actual scientific fact.
- Diabolical Mastermind: Fu Manchu himself.
- Does This Remind You of Anything?: In President Fu Manchu the assassination of a populist political candidate recalls that of Huey Long.
- Dragon Lady: Fah Lo Suee.
- The End - or Is It?: The '60s film series (produced by Harry Alan Towers and starring Christopher Lee) would always end with Fu Manchu saying "The world shall hear from me again".
- Even Evil Has Standards: Fu, despite his willingness to mind-control, murder, and torture to gain his ends, nevertheless refuses in indulge in unnecessary cruelty and is always scrupulously a man of his word.
- Getting Crap Past the Radar: "Fah Lo," as she is called in the film of The Mask of Fu Manchu, is clearly getting off on beating the hell out of Terry ("Shan" in the novel), and it's all but stated that the only reason she doesn't rape him outright is because her father would rather use him as a bargaining chip. According to one story, her actress, Myrna Loy, responded to seeing the finished footage with "Say -- this is obscene!" The year Mask of Fu Manchu was made? 1932. Pre-code. The Spirit of The Roaring Twenties was still -barely- breathing.
- Good Hair, Evil Hair: You will never, ever see a good character with a Fu Manchu mustache. Unless he's a Klingon.
- Green Eyes: Both Fu and Fah Lo Suee have 'em -- somewhat improbably.
- High Heel Face Turn: Karamaneh
- I Gave My Word: Both Fu Manchu and Nayland Smith both believe a man should keep his word even to an enemy.
Nayland Smith: A servant of the crown in the East makes his motto: "Keep your word though it break your neck!"
- Karma Houdini: Fu Manchu -- which made him a problem character under the Hays Code.
- Majored in Western Hypocrisy: Fu Manchu was an early character of this type.
- Master Poisoner: Fu Manchu is a master of many insidious and undetectable Oriental poisons.
- No Celebrities Were Harmed: In The Drums of Fu Manchu "Marcel Delibes" represents Leon Blum, "Monaghani" is Mussolini, and "Rudolph Adlon" is a creepily sympathetic portrait of that other guy with a moustache.
- The Triads and the Tongs: Fu Manchu is often depicted as controlling or at least working with these groups.
- Villain Based Franchise: There's a reason why the titles of nearly every novel, film, and show in the franchise contain the name "Fu Manchu" instead of "Nayland Smith."
- Wicked Cultured: Fu Manchu.
- Xanatos Roulette
- Yellow Peril: The Trope Codifier.
- The Moustache is a bit of a Beam Me Up, Scotty -- in the original books he was clean-shaven.
- so spelled in every novel after the first one