I'll give the serious answer, because apparently nobody else wrote it.
Bear cavalry is a no-go for about the same reason that we do not raise bears for meat. After all, a bear can be fed with just about anything, and grows quickly, and thus should be a good source of food. But it has a big drawback, which is that bears don't tolerate well other bears. You cannot make a herd of bears (however awesome it would be). There is a nice analysis of the conditions of domestication of animals for food production in Jared Diamond's Guns, Germs and Steel, which cites several animals as counter-indicated, for various reasons. Bears are the example of an animal that you cannot put in groups.
Of course there are other reasons why bear cavalry would be challenging, as cited in other answers: management of hibernation, difficulty of fitting a saddle on an animal whose weight can triple over the year (they really thin a lot during hibernation), possible low tolerance of the spine to the pressure from a rider... but all of these could probably be overcome. The impossibility to keep bears together is a much bigger problem, which prevents assembling a significant bear cavalry squadron. At best, you could have a couple of scouting bears.
(Bears are remarkably good at moving across difficult terrain, so they could make good scouts in mountainous areas.)
Edit: I thought I would add a few extra details. We must make a difference between species.
Polar bears (Ursus maritimus) are mostly carnivorous, and very hard to tame; they see humans as a potential food source (they prefer the taste of seals, but they will still happily munch on human meat). There is currently, to my knowledge, a single tame polar bear in the World; she is used occasionally for movie shots, but even though, they keep her out of fight scenes in case the instinct takes over (I read these details from this book).
Brown bears (Ursus arctos), including grizzlies, are your best bet for taming. They are huge but relatively gentle. Their diet is also at least 75% plants, and they are really not picky. They are also very tolerant to long periods without food, because that's what they do when hibernating. A grizzly can behead a human with a single paw blow, but it usually won't bother, and does not crave human meat.
Black bears (Ursus americanus for the American species, and Ursus thibetanus for the Asian one) are smaller than brown bears, and a bit more irascible, so they would be second choice for cavalry. They might be more useful as enlarged versions of attack dogs; they also have a very keen sense of smell so they could possibly be used for detection rather than charging.
Giant pandas (Ailuropoda melanoleuca) need fresh bamboo shoots. They are totally inept at many things, and it is very puzzling that they have not gone extinct already.
The other kinds of bears (spectacled bears, sloth bears, sun bears) are smaller and mostly tree-dwelling; they won't be comfortable on the ground, which makes them unsuitable for military purposes.
Of course, there is always the joker of a bear that knows Kung Fu.