In the on-line file-caching problem problem, the input is a sequence of requests for files, given on-line (one at a time). Each file has a non-negative size and a non-negative retrieval cost. The problem is to decide which files to keep in a fixed-size cache so as to minimize the sum of the retrieval costs for files that are not in the cache when requested. The problem arises in web caching by browsers and by proxies. This paper describes a natural generalization of LRU called Landlord and gives an analysis showing that it has an optimal performance guarantee (among deterministic on-line algorithms). The paper also gives an analysis of the algorithm in a so-called ``loosely'' competitive model, showing that on a ``typical'' cache size, either the performance guarantee is O(1) or the total retrieval cost is insignificant.