Dropbox allows you to pause and resume syncing through the Dropbox menu in your system tray or menu bar.
When syncing is active, Dropbox will try to be smart about the amount of bandwidth it uses. Dropbox will use any remaining bandwidth available to download changes and only 75% of available bandwidth to upload changes. You can also adjust your bandwidth usage through the Dropbox desktop application's preferences.
If you'd like to stop Dropbox entirely, you can do so through an option in your Dropbox menu.