Welcome to Muppet Wiki!
The Wonderful World of Pigeons is Bert's favorite TV show, which, as the title implies, is a show about pigeons. In Episode 0406, when Bob, Ernie, Bert, and the Kids play a game where they mention things that everybody does, Bert says that everybody likes to watch "The Wonderful World of Pigeons", but Ernie says that he hates that show, and Bob says that he never watches it.
In an early Ernie and Bert sketch, Bert, Ernie, and Herry Monster all compete for the television chair. When they realize that they can all fit in the chair together, Herry and Ernie ask Bert what they are watching. When they learn that "The Wonderful World of Pigeons" is on the TV set, Ernie and Herry leave. In another sketch, Bert informs Ernie that he was watching "The Wonderful World of Pigeons" when all of a sudden a letter H appears on TV, interrupting the program.