Dogs have been trained to guard/protect, herd, hunt, search/rescue, assist (e.g. guide dogs for the blind) and perform circus tricks, obedience or agility classes. To many, this is a clear sign of their intelligence and the superiority of the canine intellect over feline intelligence. Cats have been trained to perform tricks as seen on films or TV advertisements, but do not have the same repertoire as dogs. This leads to the obvious conclusions that cats are neither intelligent enough nor co-operative enough to be trained.
For example, in experiments where cats and dogs were expected to navigate mazes, most cats performed badly. Dogs soon learned to navigate the maze and reach the reward. Cats sat down and washed. They investigated blind alleys. They did not complete the maze in the allocated time and were therefore judged as "failing the test" or "lackadaisical". Eager-to-please dogs learned that they got a reward for learning the maze. Cats are not motivated in this way. Being opportunists, investigating every blind alley made sense to the cat - after all, who knows where prey might be hiding in the real world? Sitting down and washing is a displacement activity when a cat is uncertain.
Most of the canine activities rely upon manipulating canine social instincts. Dogs live, hunt and play in hierarchical social packs headed by an alpha male and alpha female. They frequently co-operate in raising/guarding the alpha pair's young and co-operate to hunt large prey. Juveniles beg submissively for food from adults. They are eager to please/appease pack-mates in order to remain part of their pack and they demonstrate submissiveness to higher ranking animals. Domestic dogs view humans as dominant pack members so they are eager to please us. In addition, dogs have been selectively bred over hundreds of years to enhance some traits and reduce or eliminate others.
Cats, meanwhile, have a different social structure. Where food is plentiful they are largely solitary although females, usually related ones, may form social groups. Males tend to roam in search of females rather than remain as part of a group. Where food sources are localised (e.g. a rubbish dump) they form colonies but the social structure is more akin to that of lions - groups of females who may co-operatively raise young. Unlike lions, cats do not generally hunt prey larger than themselves and rarely hunt in pairs or groups. Cats are, therefore, independent rather than truly social and have little or no need to co-operate with other cats. Feline co-operation with humans is limited unless it serves the individual cat's interests to perform a task. Whereas dogs have been bred for utility, cats have been bred solely for appearance.
Dogs are largely motivated by the pack-living instinct i.e. they will perform purely for praise and acceptance dished out by the dominant pack member (i.e. the owner or trainer). They will also perform because, in the wild, they risk being driven out of a pack or being demoted to pariah position.
Cats are not motivated by social status factors. To train a cat you must find out what motivates it. Usually this means food, or at least conditioning it that there is the promise of food at the end of the session. Even then, cats are not motivated by food in the same way as dogs - if achieving the food reward is too much hard work, cats frequently cut their losses and go in search of easier "prey". In the wild, it makes no sense for a solo hunter to expend more energy on finding or killing prey than it gets from eating that prey. While dogs will track and pursue prey over long distances and wear down their quarry, cats hunt by waiting in ambush and pursuing prey for short distances only. Starving a cat does not make it easier to train either, cats are better than dogs at ignoring hunger pangs. For young cats, although food is a powerful reward, activities such as manipulation of simple objects such as a ball or scrunched up paper, or the chance to explore an unfamiliar space can be adequate rewards in some tasks. There will always be some cats who not only learn easily, but appear to relish learning, though these are the exception rather than the rule.