I have been working with the ftp client Filezilla for some time now and switched to release candidate three of the new and upcoming Filezilla 3 just recently. I have to use ftp clients on a daily basis to upload files to my websites and edit php and html files that are already on them. They are indeed useful for webmasters but on a decline when you take a look at all Internet users - my opinion but supported by the fact that most modern browsers support ftp downloads as well.
Filezilla comes with all the options and settings that one would expect from ftp software: It supports ssl and sftp connections, offers proxy support, upload and download queues, a comfortable site manager with import and export function, resume feature, keep alive system and custom commands.
It is furthermore possible to export and import sites which is a great feature if you have to use the ftp client on more than one computers. I was not able to spot any difficulties with this release candidate; If you want to be on the same side download Filezilla 2 instead.
Update: FileZilla development continued in recent years. The latest version at the time of writing (February 2013) is version 126.96.36.199 which you can download for Windows, Mac and Linux systems or as a source code directly from the project website.
The core functionality and interface has not changed a lot though. You can still use the quick connect feature to connect to an ftp server of your choice right from the main window of the application, or connect to one of the servers that you have added to the program permanently. The program displays local files on the left and remote files on the right, with folders and files separated in two different panes.
The transfer log is displayed at the bottom of the screen. You can add new servers to the program with the Ctrl-S shortcut which opens the server manager. Here you can configure as many ftp servers as you want. Each server you add here becomes available permanently in the program.
The latest version supports a couple of advanced features like IPv6, remote file search, logging to files or a network configuration wizard.