Popular content is frequently replicated in multiple servers or caches in the Internet to offload origin servers and improve end-user experience. However, choosing the best server is a nontrivial task and a bad choice may provide poor end user experience. In contrast to retrieving a file from a single server, we propose a parallel-access scheme where end users access multiple servers at the same time, fetching different portions of that file from different servers and reassembling them locally. The amount of data retrieved from a particular server depends on the resources available at that server or along the path from the user to the server. Faster servers deliver bigger portions of a file while slower servers deliver smaller portions. If the available resources at a server or along the path change during the download of a file, a dynamic parallel access automatically shifts the load from congested locations to less loaded parts (server and links) of the Internet. The end result is that users experience significant speedups and very consistent response times. Moreover, there is no need for complicated server selection algorithms and load is dynamically shared among all servers. The dynamic parallel-access scheme presented does not require any modifications to servers or content and can be easily included in browsers, peer-to-peer applications or content distribution networks to speed up delivery of popular content.