Theoretically, is domestication of (virtually) any animal possible?
As the previous answers clarify, all organisms have heritable traits that may be manipulated through selective breeding. It is the pragmatics that can be prohibitively challenging. From an (zoo)archaeological point of view, few animals have actually been domesticated, and only recently in our species' history. The dog is an unusual case, perhaps domesticated 14,000 years ago; most domesticated animals only show skeletal changes within the last 10,000 years. Cats, compared to livestock's total dependence on humans, are 'barely' domesticated--they got used to humans while camping out in Egyptian storehouses where all the mice were, perhaps around 4,000 years ago, but even today a fluffy house cat will revert to a feral state if abandoned. 

Many animals are behaviourally unsuitable for domestication. If an animal is dangerously aggressive, for example, they cannot be penned and isolated--so the many controlled generations it takes to reduce their baseline aggression cannot occur. Humans also tend to co-opt pre-existing social structures in a species, such as becoming the 'alpha' in a dog pack or the head 'ram' of a sheep herd. Species without a hierarchy or herd mentality are difficult to control and keep track of, and so do not lend themselves to human care. 

You mentioned tigers in your question. Tigers have little to offer people (other than pelts), they're massive/aggressive, and they're jungle loners. You can't raise a herd of tigers; they'll kill each other and the survivor will kill you. That they're carnivores is also challenging, since a carnivore is much more expensive to feed than a bunch of grass-munching sheep. Altogether, there was never a situation in prehistory that would have turned tigers into giant house cats. House cats eat unwanted mice; tigers eat your cattle (and children). The occasional tiger 'pet' won't change that. 

Domestication, outside of recent experiments (like the Russian foxes mentioned above), has always been a protracted, indirect process. People started interfering with animals that were already useful in some way(s). Dogs offer warmth, hunting aid, defence, transport, and (in a pinch) food. Alligators, tigers, and sharks are not useful enough to make the danger and cost of raising them worthwhile. Even if you did eventually produce a 'human-friendly' shark, there would still be a 'wild' population ready to eat you--and your complacent pet sharks, too!

For a very readable explanation, try the chapter on domestication in Jared Diamond's (1997) Guns, Germs, and Steel.