I had the chance to play around with the Drupal IMCE module in the last couple of weeks, and was impressed. It's a slick module that lets your users manage their own folder, upload files, etc. The user interface is pretty cool, and it's all handled through AJAX so you never navigate away from the page. You can set allowed file types, user memory quotas, etc.
By default you can only upload one file at a time. I needed to upload files in bulk, so I installed the IMCE SWFUpload module.