Gang of Critters

When The Smurfs invaded America in the early 1980s, or even way back when they were created in Belgium in the late 1950s, they spawned a grand tradition of cute creatures with silly names who hang out in groups and get into all manner of misadventures, then get out of them again through The Power of Friendship.

Anime

 * Monchichis. Originally a toy line.

Film

 * The Ewoks from Return of the Jedi, who later got two (made-for-TV) movies and an animated series of their own.

Live Action TV

 * The Fraggles of Fraggle Rock
 * The Wombles, a British example. Remade as an animated show decades later.
 * Teletubbies.

Toys

 * The Astrosniks, a German toy set.

Webcomics

 * Achewood parodies and subverts this one hard. The cast consists of anthropomorphic cats and talking stuffed animals; but one of the stuffed animals is an elderly disaffected teddy bear, one is a psychopathically alcoholic stuffed lion, one is a milquetoast bear with the occasional delusion of grandeur, and one is a five-year-old otter who only exists to be scarred psychologically. Of the three cats, one is a Rich Idiot With No Day Job, one is a severely depressed coder, and one is a nutjob holier-than-thou pseudo-activist who only finds meaning in putting down everyone around him.
 * Bear Nuts is another webcomic subversion of this. An Affectionate Parody of Care Bears, except with characters like Prozac and Evil bear.

Web Animation

 * The Happy Tree Friends. Subverted in that they end up dying horrible deaths in every episode.

Western Animation

 * Care Bears
 * The Get Along Gang
 * Gummi Bears
 * My Little Pony
 * Shirt Tales
 * The Snorks, also based on a Belgian comic strip.
 * The Suntots, from The Smoggies.
 * The Wuzzles.
 * Winnie the Pooh and friends qualify, although it was less pronounced in the original books.
 * The Happy Little Elves from The Simpsons.
 * Rainbow Monkeys from Codename: Kids Next Door.
 * Dummi Bears from Rugrats.
 * The Buddy Bears from Garfield and Friends are a vicious parody of this trope.
 * The Schlubs from The Grim Adventures of Billy & Mandy.
 * The Gigglepies from The Fairly OddParents.
 * The Woodland Critters from South Park.
 * Squishy Bearz from Eek! The Cat.
 * The Biskitts
 * The Paw Paw Bears (with extra Braids, Beads, and Buckskins)
 * Monchichis also had an American cartoon (with a hideous Ear Worm of a theme song)
 * How can anyone forget Chucklewood Critters?
 * Blinky Bill
 * The main cast of Littlest Pet Shop.
 * The Bluffers
 * Kissyfur
 * Ovide and the Gang. Heck, it's right there in the title.
 * Forest Friends
 * Chucklewood Critters