When you upload a file to Dropbox, it's first sent in its entirety to Dropbox's servers and then downloaded to any synced computers. In a new experimental version of Dropbox, however, you can enable streaming sync that starts downloading on the target computer while you upload.
The new desktop client (version 2.9) allows users to download files as they're being uploaded to Dropbox. Only the downloading machine needs to be updated to 2.9, so using the experimental client should speed up downloads for shared folders as well as from your other devices, regardless of whether anyone else upgrades. As a bonus, the new client also allows you to scroll through the "Recently changed" tray pop-up now scrolls so you can see more than just the last three uploaded files.