Max (the Grinch's dog)

From Muppet Wiki

Max, the Grinch's dog, was a recurring character on The Wubbulous World of Dr. Seuss. Like the Grinch himself, Max originated in the 1957 Dr. Seuss book How the Grinch Stole Christmas. The good-hearted, much maligned dog assists his mean master with much reluctance

On Wubbulous World, Max appeared only sporadically, debuting in the fifth episode, "The Guest", as performed by Kathryn Mullen. Stephanie D'Abruzzo took over for the dog's two other season 1 appearances, and for season 2. He was the central character in "Max the Hero", saving a child's life and going to live with Mayor Stovepipe for a time.

In "The Grinch Meets His Max," it was revealed that the Grinch took Max in as his pet when Max started scratching an itchy part of the Grinch's back that he couldn't reach.