Comedian Bob Monkhouse as the Asshole Victim Sylvester Le Fley in "The Scented Room" - Monkhouse later used this as an example for his comment "my non-comedic acting roles tend to be the sort of person who would keep their cocoa warm by burning down an orphanage".
The Other Darrin: Adam Klaus was played by Anthony Head in the first episode but he had to drop out owing to his role in Buffy although his photo appears on Adam Klaus t-shirts and posters throughout Series One. From Series 2 onwards he's played by Stuart Milligan, and appears in pretty much every episode.
The Pete Best: Stuart Milligan is considered the definitive Adam Klaus, particularly since Anthony Stewart Head only played him in the pilot episode.
A straighter example is Maddy's cameraman boyfriend from the pilot (played by Alistair McGowan) who was intended to become a recurring character, but is never mentioned again.
Hugh Laurie was actually cast at one point before the pilot was filmed, but left the project because of Jonathan's reluctance to solve crimes — Laurie couldn't find the character's motivation for actually following Maddy on her investigations. Somewhat ironic, given that House is something of a Dr. Jerk Jonathan Creek - obsessed with puzzles, not so much with people.