Beary Funny

Everything's Worse With Bears...except when it isn't. Perhaps it's because of the proliferation of the teddy bear as a child's toy, but bears are often portrayed as Boisterous Bruisers or sometimes just Big Fun, and aren't really looking to eat people so much as just looking to eat. (Truth in Television; most bears are omnivorous and will gladly eat nuts and berries; also, while grizzlies are aggressive, their favorite food is salmon.) Seems most common in Western Animation, although circus bears are common in Real Life.

Note that while the majority of these have bears being used for comedic purposes, non-comedic examples of bears being lovable should work for the trope as well.

Examples of Beary Funny include:

Anime and Manga

Shirokuma Cafe has Panda and Polar Bear as two of its core characters. Polar Bear is the owner of the titular cafe and is a Pungeon Master. Panda is a rather lazy Cloudcuckoolander who is a regular patron.

Advertising

Coca-Cola's famous commercials featuring polar bears that they bring out every year around the holidays.
- In late 2011, they even released special-edition red-on-white cans (instead of the traditional white-on-red) as part of a "Save the Polar Bears" campaign.
Rival Pepsi has used bears for a Super Bowl commercial on a couple of occasions.
Fedex studied recent Super Bowl commercials to come up with the ten factors needed for the best commercial ever. It involved Burt Reynolds getting kicked in the nuts by a talking bear (product message optional).
Charmin toilet paper ads.
The Sugar Bear (orignally three Sugar Bears) from the Sugar Golden Crisp cereal boxes.

Comic Books

In the French graphic novel Pyrenee the Wild Child title character is a girl raised by a bear in the mountains. The bear is mostly seen as a big furry dope, but there's one scene where they get into a serious argument and he only just manages to hold back from killing her.

Film (Animation)

Baloo in The Jungle Book epitomizes the "lovable lug" archetype for bears. Baloo was also friends with Mowgli in the original Kipling story, but his Disney version is probably the most well-known.
Little John in Disney's Robin Hood, practically an Expy of Baloo.
Boog the bear from Open Season.
In another example of bears being nice, the movie Brother Bear begins with Kenai discovering that his spirit animal is "the Bear of Love". And then he tries to prove his toughness by slaying a bear and gets turned into one as a result, and discovers that bears are pretty nice.
Bongo the Bear from the first segment of Fun and Fancy Free.
Cubby from Peter Pan, who wears a bear suit as clothing.
Brer Bear from Song of the South. He's a villain, but a harmless and humorous one.
Muk and Luk the polar bear twins from Balto.
Zozi from Bartok the Magnificent.
The second half of the upcoming film Brave apparantly had the entire royal family save Merida (whether King Fergus is affected by this or not is debatable) being turned into bears.

Film (Live Action)

Disney's Escape to Witch Mountain (1975). Tia frees a captured bear, which goes along with Tony and Tia and protects them.
The bears in the movie based on the Country Bear Jamboree, The Country Bears.
In Sadko, The Big Guy proves his strength by wrestling a bear. When the Mystery Science Theater 3000 crew riffed on the film, they turned this scene into the bear staging an intervention and giving the guy a hug.

Literature

Winnie the Pooh, being based upon a teddy bear, is lovably dim and goodhearted, and is often thinking about honey.
Gentle Ben
The Berenstain Bears
Paddington Bear.
Little Bear.
While the Hoka can be bad for the mental health of those dealing with them, they're very well-meaning, kind-hearted beings.

Live Action TV

Cookie Bear from The Andy Williams Show.
Gentle Ben.
Kintaros of Kamen Rider Den-O is partially based on a bear; for the most part he Does Not Know His Own Strength, a bit clumsy, and a Gentle Giant all in one package.

Newspaper Comics

The Far Side depicted bears sympathetically, even (or especially) when they go after humans.

Puppet Shows

Fozzie Bear from The Muppet Show.
- Bobo from Muppets Tonight. Although larger and with a more intimidating role as security guard, he's just as big a softie as Fozzie, if not more so.
Baby Bear from Sesame Street.
Bear in The Big Blue House.
The Bear in the Flying Carousel from The Teletubbies, unlike that other bear from that show.

Real Life

The Trope Codifier is the actual teddy bear, invented in 1902 in reference to an incident where Teddy Roosevelt refused to kill a bear that had been captured and tied up for him to "hunt".
Trained bears are common performers at circuses, enough so that they named a trope.
And, of course, pandas have always been immune to the usual depiction of bears, even though they're really just as dangerous as other bears are.
Behold: Bears racing monkeys on bicycles. Is it not awesome?
The Polite Bears!

Theme Parks

The Country Bear Jamboree at Disneyland and Disney World. Bears playing musical instruments! And singing!

Video Games

Tae the Bear God of Lusternia. He has a Little Guy Big Buddy relationship with his (much brighter) friend Bollikin, and spends most of his time playing with his bear creations and eating honey. He still shouldn't be messed with, though.
Teddie in Persona 4.
Banjo from Banjo Kazooie.

Webcomics

Sore Losers has a blue midget bear named Coleman as its Animal Mascot. While Coleman still can be vicious, he's also a constant source of comic relief, talks in half-growls, and is small enough to pass for a teddy bear when standing still.
When some bar-bear-ian Were-bears turned up in Exiern they unleashed a Hurricane of Puns, utterly un-bear-able in the watching crowd.

Web Original:

Beary, Benzaie's son/brother who also happens to be a plush polar bear, and usually winds up as The Woobie thanks to the way Benzaie treats him.
The Bear FAQ
Juuichi from Morenatsu, despite his usual expression.

Western Animation

Baloo again in Tale Spin, as well as Rebecca, Molly, and Kit.
Yogi Bear, Boo Boo, and Cindy Bear.
The Care Bears, although these probably fall squarely into the "actual teddy bears" category.
- Likewise, the Dummi Bears from Rugrats, who are an obvious spoof of this, though their name is an Homage to...
The Gummi Bears, who also might qualify--although, as they had a wide variety of personalities and everyone was a bear, maybe not as much so.
In the Teen Titans episode "Bunny Raven, or How to Make a Titanimal Disappear", Cyborg gets turned into a dancing bear, in a tutu. Due to the magical properties of the realm they were trapped in, every time he removed the tutu, a new one winked into existence to replace it, resulting in a giant pile of discarded tutus.
The unnamed bear that appears very often in Harvey Birdman Attorney At Law.
Humphrey Bear from the Classic Disney Shorts.
Bear from Word World.
Tim, Arianna, and their son from The Cleveland Show.
The Little Flying Bears.
Julie Bruin from Tiny Toon Adventures.
In The Simpsons, Homer Simpson thinks the ballet is a bear wearing a fez and riding around a tiny car.
Rupert Bear
ThunderCats (2011) has Cute Machines the Ro-Bear Berbils, helpful, rainbow-hued robotic teddy bears who love to build and repair things.
The Hair Bear Bunch.
Breezly Bruin, a Hanna-Barbera character from 1964 who always tried to get into an arctic army base.