Should You Clean Out Nestboxes in Your Garden?

For our garden birds, the breeding season is now over. The nestboxes in our gardens that a few months ago were home to hungry broods of blue tits or house sparrows now lie quiet and empty. Well, not quite empty. They will still contain the nesting material used by the previous occupants. Should you just leave it in there over winter or clean out nestboxes in preparation for new birds next spring?