This page is for just about any example of puppets (but not Muppets or other Henson productions) that appear in otherwise live-action TV, movies, music, etc. I'm sure there are any number of examples that I've forgotten, and many more that I've never seen.
Apollo, Apollo (TV scene) from a season 3 episode of 30 Rock
Avenue Q (theater)
Biutyful (music video), by the Weirdos & Coldplay
Boost Mobile (TV commercial)
The Colbert Report (TV scene) from Nov. 28, 2012 episode
Count It Off (music video), by The Saturday Knights
Dancing's Not a Crime (music video), by Panic! At the Disco
Greg the Bunny (TV series)
Halloween Hugs (short film)
The Happytime Murders (feature film)
Intro to Felt Surrogacy (TV episode), from season 4 of Community
It's You (music video), by Wax
Land of Confusion (music video), by Genesis
LazyTown (TV series)
Learning Town (web series)
More Dumb (music video), by Durry
Puppet Show (TV episode), from season 1 of Odd Squad
Smile Time (TV episode), from season 5 of Angel
Spitting Image (TV series)
Truth Anti-vaping campaign (TV commercials) I'd like to link to a playlist of these, but I couldn't find one.
Wonder Showzen (TV series)