"Prisoner of Zenda" starring Peter Sellers, Peter Sellers, and Peter Sellers. My favorite character in this movie is actually Count Rupert of Hentzau, played by Stuart Wilson.
Both movies are very entertaining comedies, plus the added pleasure of having the support of Henry Mancini background and theme music.
I always liked this movie. In the Conan Doyle stories, Watson is portrayed as an intelligent, brave, and perfectly competent man, albeit not a genius like Holmes. Somehow, "not a genius" got turned into "complete idiot" by the Baker Street Dozen and lots of other film adaptations. So "Without a Clue" inverts the premise by making Holmes the idiot - a clever move!