SaveMyInbox is yet another useful web application that can come real handy for some folks.
The service connects to your Gmail and Dropbox account. And then it would routinely check your mailbox and extract attachments and save them to your Dropbox.
This is a good way to backup file attachments from Gmail in case you like to keep it clean.
SaveMyInbox is a simple webapp that will automatically save your Gmail attachments to your Dropbox, enabling you to check them offline without having to remember which ones to save.