Dropbox is great for syncing files if you have the rights to install Dropbox on the machine you’re using. If you don’t, URL Droplet can fill a gap by allowing you to easily save web-based downloads to your Dropbox account.
It’s a simple tool to use. Visit URL Droplet, authenticate your Dropbox account (this happens with Dropbox, not by giving your login credentials to URL Droplet), and then begin plugging in file URLs into the URL Droplet interface. Files you enter there are synced to the root directory of your Dropbox account. The only limitations are the amount of space you have in your Dropbox account and that the files are saved only to the root (although you can rename the files before sending them to your Dropbox).
URL Droplet is a free service; hit up the link below to take it for a test drive.