For instance, there is a condition where people are born without a corpus callosum - the large bridge of connections between the brain halves. This is sometimes severed as a treatment for severe epilepsy, and gives rise to a range of quite obvious (and fascinating) side effects.
But for people born without, the effects are almost nonexistent (the main one, according to a researcher studying this, is a relative slowness of learning nouns as a child). In fact, it used to be believed that this condition was very rare (less than a case in a million is what I heard). But now, with MRI scanning and other tools, we now know it's actually up to one in a thousand. The brain managed to compensate with other, subcortical, connections during development.
In a similar vein, I've read about cases with a patients born entirely without one hemisphere; and recently there was news about a woman found to have no cerebellum at all - and the cerebellum contains about 80% of all neurons in the human brain.
But note that while the people above led normal lives, they where not asymptomatic. They show various symptoms and defects (the decerebellar woman apparently had clumsy, uncertain movements). Similarly, I have not seen anyone claim these hydrocephalics are asymptomatic either.
And - this is my speculation - I would not be surprised of these patients are a lot more susceptible to problems as they grow older. Their brains likely have much less margin for error, and damage from small strokes, or developing brain disorders that would go unnoticed in you and me would show up clearly for them.