Dropbox is a free and extremely easy-to-use tool for sharing files and syncing them between computers, and you can also use Dropbox to back up files and access them from other computers and devices (including from your iPad or iPhone, with dedicated apps for each of those devices).
Dropbox's interface is largely invisible, which is part of what makes this app so easy to use. When you install Dropbox on your Mac or Windows machine, you create a Dropbox folder. This is a local folder that lives on your desktop, but you can access the folder from other computers (Macs or PCs), or from anywhere you have access to a Web browser.
Even better, you can use this folder to share files with other people--either through a designated Public folder or by setting up folders inside your Dropbox with shared access by multiple users that you choose (this solution can be particularly useful in work settings as a productivity tool, especially because Dropbox tracks older versions of files). You can also use Dropbox to back up your files online, although the biggest barriers to this are the size of your backups (you get 2GB free with Dropbox, or up to 100GB with a monthly fee) and the fact that backup files need to be located inside your Dropbox folder, although there are some workarounds for more technically savvy users.
Dropbox gives you a lot of useful features for free, with a remarkably smooth interface and shallow learning curve. If you find yourself frequently transferring files between different people and computers via e-mail or USB drives, Dropbox is a must-download.