There is a big fat book from the British Academy that lists all the medeival and renaissance library catalogues still extant. They have got through ten volumes now and at least five more are in the pipeline. The latest volume to come out has been the one on the Colleges of Cambridge University (I impatiently await the Oxford edition) which I hav found very useful for my research.
The point of all this is that it allows us to see just how completely random the survival of books and manuscripts is, as well as how it is usually bad luck or neglect that causes us to loose them. For instance, not one of the large collection from Clare College's medieval library survives because the fellows made off with the books when they thought the college was about to be closed in 1549. This was after the library had survived a terrible fire in 1521. Likewise, nothing remains of Queens' College's ancient library. On the other hand, Pembroke College and Peterhouse still hold up to half the books found in their catalogues dating from the Middle Ages. It used to be thought that there was some sort of systematic library clearance by the Protestant reformers (and their may have been in a few cases at Oxford) but in reality the losses are due to carelessness, theft and throwing out stuff that was not considered useful anymore. Very many medieval manuscripts were binned as soon as a printed version of the same book was available.
This explains why we have so little left from the ancient past. If Pembroke College can loose half its manuscripts in a few hundred years when it has a library that was never ransacked or suffered large scale damage, what hope was there for the libraries of Alexandria and Rome when both cites have been sacked, razed and taken by endless invaders and rioters. And last year, in Baghdad, as my correspondent below notes, the national library went up in smoke. This was not due to any deliberate policy but just due to the break down in law and order which accompanied the occupation.
The lesson of the losses at Cambridge from a secure and academic environment without the risks of war, is that we don't need to ask how libraries are lost. The more interesting question is how on earth anything has survived for as long as it has.