The programmes, which last year included the 100 Greatest Stand-Ups, 100 Greatest Toys and 100 Greatest World Cup Moments, have been axed by the broadcaster's new chief creative officer Jay Hunt.
The Guardian reports that Hunt, who joined Channel 4 from BBC One several months ago, has told colleagues that the genre has reached the end of its life.
"It is felt that they are popular but we can be doing bolder and different things rather than something which is fun but which some people feel can feel a little spurious," a source told the paper.
Money saved by axing the clip shows will apparently be put back into producing original programming, with a focus on comedy.
However, Alex Zane's Rude Tube will be kept, while one list show 50 Worst Weddings will still be broadcast next month as part of Channel 4's coverage of the royal wedding.
The insider added: "The Jonathan Ross rundown of the nation's favourite toys did well last year and if Jonathan comes up with an exceptionally brilliant idea like that we may do it. But the direction of travel is now very much not to do them anymore."
Ross's Christmas toy rundown was watched by 2.43m viewers when it aired in December.