The flavor text for the card Grizzly Bears reads Don't try to outrun one of Dominia's grizzlies; it'll catch you, knock you down and eat you. Of course, you could run up a tree. In that case, you'll get a nice view before it knocks the tree down and eats you. In the early days of Magic, a 2/2 creature with no abilities cost 3 mana, 1 of the creature's color and 2 of any color, while the Grizzly Bears (also 2/2 with no abilities) is only 2 mana; 1 green, 1 other. Thus, they're faster.
Other Bears in Magic include Werebear (starts off a weak 1/1, but get seven cards in your graveyard and it turns 4/4), Ashcoat Bear (you're not even safe from your opponent summoning bears during your turn), and Bearscape (they can come from anywhere!)
The bears of Tarkir are even worse news than usual since they start at power 4 and weigh somewhere around a ton. The Khan of the Temur, Surrak Dragonclaw, earned both his position and his many scars by fighting one, which is an achievement roughly on par with stopping an oncoming car by punching it. This changes somewhat in the plane's new timeline, as the return of the dragons knocks the bears down several pegs in the food chain, especially since dragons are noted to find bear flesh quite tasty — although this has the side effect of winnowing the bear populations down to the absolute meanest, fiercestand most battle-hardened bears around.
Dishonored Roleplaying Game: Tyvian bears are described as having fangs the length of a man's arm and claws that can puncture metal, and local folklore holds that they are literal embodiments of the island's brutal and unforgiving wilderness.
What's the biggest, strongest werecreature? That's right — the werebear. In defiance of the "bad news" aspect, however, werebears are the only good-aligned lycanthrope (besides were-ravens, but they seemed to not fit in with the others, being divine creatures in at least a sense), being Chaotic Good prior to D&D 3.5 and Lawful Good after. This was probably thanks to Beorn.
Werebear-ians: Barbarian Werebears. Ouch.
There's a Running Gag about Dungeons & Dragons druids: no matter how good their stats, they will invariably reach level 5 as a human/elf/whatever, then spend the rest of their lives as a bear because the Natural Spell feat lets them still cast spells while in that form. To take this even further, they have animal companions as well. So this means that they can transform into a bear (Wild Shape) and ride a bear (Animal Companion) while summoning bears (spontaneously cast summon spells). Oh, Crap!.
Most templates in 4e have a requirement of a certain creature type being necessary in order for it to apply, usually humanoid. However, the Death Knight template's only requirement is that the creature be level 11, which means Cave Bear Death Knights are realistic possibilities in any campaign.
In 4th edition, the Druid class gains at 1st level the ability to change into animal form (which doesn't technically change your stats, it just makes you look different and gives you different attacks) at will for as long as you want. So, technically, you could play a Druid who spends their entire life as a bear.
Plus, there's a spell in 3.5 edition called "Bite of the Werebear", which grants +16 strength, +8 CON, three natural attacks, and the Power Attack feat to the target. It has a range of self, but can be cast on familiars for... interesting results.
There are also the extremely popular owlbears, which are Exactly What It Says on the Tin, and come in normal, polar, and Pelor save us all, winged. Notably, owlbears take the "bad news" part further than most, as they're noted to be incredibly violent and savage, due in large part to their anguish at being a blend of bear and owl.
This is definitely the case for the enemies of Breland, considering the Brelish field elite bear cavalry (as befits Breland's coat of arms). Obviously, the Brelish themselves would tend to disagree.
5th Edition allows certain druids to take on much more dangerous forms at lower levels, allowing a druid to turn into a grizzly bear at level 2 and an even scarier polar bear at level 6.
"Bad news" depends on who you are. Just to remind the forces of evil that good is not just feathery-winged angels, there are the bear-like Lawful Good Warden Archons. For extra fun, there are also the Neutral Good Ursinal Guardinals, who are not only celestial super-bears, but are also wizards as well! To spread the fun around, the Book of Exalted Deeds introduces the prestige class the "Sentinel of Bharrai" for Ursinal-revering mages who want to escape the problem of Squishy Wizard syndrome. Among other things this class allows them to turn into bears, and eventually into dire bears, at will!
Bears, polar bears and dire bears (identified here as cave bears or short-faced bears from Real Life prehistory) are carried over from D&D, and are of course very powerful, dangerous and aggressive beasts. D&D's werebears are also present.
The kokogiak is a titanic — around elephant-sized — ten-legged polar bear originally from Inuit Mythology. They're intelligent enough to understand morality and thus have an alignment beyond True Neutral, and of course, they're Neutral Evil as a rule. They are monstrously aggressive and openly sadistic and are massive and powerful enough to be as cruel as they please towards whoever short of a dragon or a tribe of giants has the misfortune of crossing their path without having to worry about their victims being able to fight back. Luckily for everyone else, they're fairly uncommon and only found in isolated areas of the Grim Up North.
Pathfinder hits bears with the nerf-bat as far as druid's Wild Shape goes. While shaping into a bear grants stat benefits on a par with other animals of the same size category, the bear chassis doesn't come with any special attack forms or defences that can't be improved on by other forms such as great cats.
Exalted: The Huraka (wind bears). While they are normally gentle wind herders, they also serve as the shock troops of the air elementals. You know you're screwed when giant, flying bears with wind powers come barreling toward you.
Old World of Darkness: What's stronger than a werewolf in its hybrid "war form"? A Gurahl werebear in their version of that same form. Not only that but the incarnation of death itself was the aptly-named Death Bear, which had to be fought to bring someone back to life. Guess which changing species was the only one up to the task? Ironically enough, the Gurahl are actually the ones who are supposed to make everything better. Just as werewolves are Gaia's warriors, werebears are Gaia's healers — they have the most potent restorative rituals of all the Changing Breeds, including the ability to bring the recently deceased back to life (but if they get there a little too late... well...)
Warriors Adventure Game: In the campaign Mission of Mercy, the cats protect a young girl who gets attacked by a bear. Notable for being the only time bears appear in the series.
World of Synnibarr takes things a step further, not only having a handful of bear subtypes with an assortment of powers (mostly-psychic based), but also a set of "Grizzlies". While they were equally dangerous, the cake goes to the Giant Flying Grizzly; eye-lasers that would instantly kill you from 200 feet, the ability to fly 100 miles per hour, and the tenacity to stalk their prey "vast distances".
World Tree (RPG): Gormoror, bear people, downplay this — they're aggressive and barbaric, but easily enough reasoned with. Churshash, however, play this entirely straight — they're very aggressive, bear-like animals driven into constant pain and rage by Wounds That Will Not Heal, their blood induces mindless fury in anyone it touches, and are generally a fair match for four well-armed and prepared warriors.
BattleTech features Clan Ghost Bear, one of the strongest Clans in the Inner Sphere. The Clan deploys huge bear themed BattleMechs such as the Kodiak and the Grizzly. They have a well-deserved reputation as The Berserker, too. They're considered slow to anger, but once someone succeeds in pissing them off they have a tendency of going into an Unstoppable Rage and tearing through whatever has gotten them mad. Even more alarming is their habit of blasting their way through everything that happens to be between them and their target, even if it's a neutral party or even an ally.
One of the specialities of the Kislevites, the game's Fantasy Counterpart Culture to the Slavs. The bear is the official symbol of the nation of Kislev and associated with its line of Tzars to the extent that they are depicted in heraldry riding one (most notably Boris Ursus). Not to mention, their Top God is the aptly named Ursun, the God of Bears, and his clergy are known to ride bears as well. As seen in both Warhammer: The Old World and Total War: Warhammer III, the Kislevites also have access to several regiments of War Bear Riders, ice sleds that are pulled by bears (some of which carry mortars), and even Kaiju-sized Elemental Bears coalesced from the ice and snow that makes up their homeland.
There's also a mention of a Chaos Lord whose chariot is pulled by skinless bears.
Also the Dogs of War character Beorg Bearstruck, a Norse barbarian that was transformed into a werebear. He leads a mercenary regiment of Norse marauders called the Bearmen of Urslo, who wear bearskins and display a bear-claw device on their shields. Beorg and his followers are all savage barbarians who revel in battle, massacre and shedding blood for the Chaos Gods, although he does also have a distant cousin called Ruprecht of Bearmark, who ran away to study poetry in Nuln...