Recently, partly due to my wife starting to run a game set in the 1920s era and inspired by much of the pulp world, and also due to my Loyal Lieutenant shana bringing a copy of the first Fu-Manchu omnibus over to our house, I have finally had the opportunity to try them.
"Imagine a man with a brow like Shakespeare and a face like Satan..."
So begin most descriptions of Doctor Fu-Manchu, the most brilliant mind on Earth (according to his adversaries), an implacable foe of Western civilisation, yet a man with full command of the science of the modern era and the mysticism and resources of the ancient world, especially those of the entire East -- not merely China, but Japan, India, and other nearby regions of the world.
Clearly strongly inspired by the adventures of Sherlock Holmes -- especially the evocative and frightening picture of the mastermind of crime, Professor Moriarty -- Sax Rohmer tells his tales from the point of view of Dr. Petrie, good friend of adventurer and agent of the Crown (near as I can tell, anyway) Nayland Smith. Especially early on, the relationship of Petrie and Smith echoes that between Watson and Holmes, with Smith displaying his greater experience and erudition and Petrie spending much of his time amazed, bewildered, and frightened.
However, the similarities are in some ways misleading. Petrie is a highly competent man on his own, and once he comes to understand the adversaries they face he is invaluable in ways that Watson generally was not. This is not, please note, to denigrate Watson's capabilities; his adventures with Holmes generally focused very specifically on the deductive brilliance of Holmes and thus really didn't showcase Watson much. In the battle against Dr. Fu-Manchu and his agents, Nayland Smith and Petrie are much more equals, Petrie merely being a newer recruit who just needs time to get up to speed. (Indeed, at one point Petrie completely outdoes Smith, succeeding partly through luck and partly through bold and correct action in getting a ringside view of a critical meeting of villains)
While the stories do, naturally, have some of the stereotyping to be expected both from their subject matter and era in which they were written, I actually found it much LESS racist than I expected. While Dr. Fu-Manchu is depicted as a villain, there is much less pervasive anti-Chinese (or other race) discussion than I thought might be there. Even Fu-Manchu himself is shown with many positive traits -- enough to make one regret his deliberate course of, um, naughtiness.
As others have also noted, there's a strong note of the supervillain and superspy cliches coming into being. Fu-Manchu has hidden strongholds, super-technology (for his era), genetically engineered (to use the modern term) monsters, and other trappings of any good Bond or comic-book villain.
Overall, they're quite fun reads. I occasionally find the hat tricks that Nayland Smith plays to be a bit too much -- unlike Holmes, who occasionally would produce some new fact but who usually had the fact's existence implied by other clues, often Smith will have entire new pieces of information about the "East" which mean that he's the only one who could possibly solve the mystery. I'm glad I've finally started reading them, though. Well worth the trouble.