If you have a Macintosh running OS X:
The best free FTP client we have found is RBrowser.

Transmit is a little more user-friendly, but will only work for a limited time before you have to purchase it for $25.

If you have a Macintosh running OS 9:
We recommend you download and install the free Fetch 3.0.3. (Read the page carefully; only the 3.0.3 version is free.)

If you have a Windows PC:
We recommend CoffeeCup Free FTP.