that's the problem - we have plenty of that. The problem is accessing the data that's stored. We have several levels of storage; some we can access at will, and others that seem only to be accessible in response to triggers.
I'm sure we're all familiar with that sensation of smelling something and suddenly being transported to a different place and/or time. We're often not sure of the details, but we know that the smell has dredged something up from deep inside one of the levels in our hard drive. Sounds do it too - particularly music. We hear a melody and it reminds us instantly of a person, a place, or an event - sometimes all three at the same time. These memories are all filed away in our brains, and although we may not be able (or want) to retrieve them at will, they're there, ready to be recalled when triggered.
This form of memory storage must be vast, and the brain seems to have a sophisticated system for tagging memories according to their relevance and importance. Some are discarded very rapidly as not at all important, which is why we don't remember the colours of the cars we saw on the way to work this morning. Pile into the back of one of those cars at a traffic light however, and you'll recall a lot more detail, and for longer. You'll eventually forget the fine detail, like the colours of cars involved, and you certainly wouldn't be able to recall the face of the other driver after a few months, but if you met that driver again six months or even a year later you would get that "I know that face" feeling.
It's all very fascinating, and the one thing we are sure of is that we aren't sure how our brains work. Probably we never will.