I should mention that the Saint (a.k.a. Simon Templar) began his career by boldly seeking out adventure, and after awhile, it began coming to him. Templar mentions from time to time (e.g. in "The Elusive Ellshaw" in _The Saint Goes On_) that he also attracts women looking for lost dogs, con men looking for a mark, and a public who generally see him as "something between a benevolent if weak-minded uncle and a miracle-working odd job man." He's adept at sorting the wheat from the chaff to find profitable adventures.
"The Covetous Headsman" (Paris) - The headless body of a shipping office clerk was found in Paris - but the decapitation took place after death. Templar uses some of his old Resistance connections to solve the mystery. Note that this isn't a mystery story as such; Templar's problems generally have only 1 suspect, and aren't arranged to ensure that the reader necessarily has a fair chance at guessing things. Incidentally, the fictional story mentioned in passing is G.K. Chesterton's "The Secret Garden", from _The Innocence of Father Brown_.
"The Angel's Eye" (Amsterdam) - A respectable-looking middle-aged couple approach Templar in a restaurant with a problem. The diamond cutter to whom they just delivered the Angel's Eye for recutting (on behalf of a firm of jewelers) now denies that he ever heard of it or them.
"The Rhine Maiden" (The Rhine) - This is Templar's private label for a girl met on a (train) journey along the Rhine - a girl with an aura of enchantment about her, traveling with her newly retired grandfather. (His ideal of a Rhine maiden is closer to the original myth than the popular image fostered by opera singers.)
"The Golden Journey" (The Tirol) - The Saint, meeting a spoiled, beautiful girl, decides to try to salvage her, by arranging matters so that she must hike overland with him to Innsbruck. While this is an unusual tack for him to take, there are precedents - "The Sleepless Knight" and "The Man Who Was Clever", for instance. Oddly enough, it also reminds me of George MacDonald's _The Wise Woman_, although stylistically they are quite different.
"The Loaded Tourist" (Lucerne) - While walking up to his hotel by the lake on a dark night, Templar fails to stop two thugs from fatally stabbing a shoe manufacturer and stealing the victim's briefcase. Following the usual investigator's tack (looking for breaks in established patterns) nets an interesting collection of observations, starting with the victim: a businessman (and looking like it) in a tourist's paradise, on the eve of his immigration to the U.S.
"The Spanish Cow" (Juan-les-Pins) - Templar doesn't rate the title of Saint here. The lady mentioned in the title is an aging, rich widow who hasn't done any harm. Templar's plan to steal her diamonds has no justification. What good he does is more accidental than intentional, at least initially. Not a bad story, but not consistent with the Saint's original swashbuckling philosophy.
"The Latin Touch" (Rome) - Back to the old Saint, fortunately. Templar casually makes the acquaintance of Sue Inverest while sightseeing in the Colosseum - only to be knocked cold when Mafia kidnappers ambush her. (The daughter of the U.S. Secretary of State, she had eluded her escort as a lark.) Fortunately, upon Templar's awakening in jail, the Secretary has not only checked his war record with the O.S.S., but is prepared to trust him rather than risk his daughter's life to cops who may be in the Mafia's pay.