FTP client
Notepad++ also has a FTP plugin(very very handy), I think it comes as a default plugin now too. Though there are no complicated features, it supports editing files directly in N++ as you would expect and will auto upload each time you save the file. That means caution should be exercised when saving files.
If you would rather learn how FTP works from command line you can use a simple command prompt. Simple type "ftp" and then you would enter "open blahblah.com" it will prompt you for login details then, from here all standard ftp commands apply. You can see the following link for those http://www.nsftools.com/tips/RawFTP.htm
For a GUI based FTP I would recommend WinSCP over filezilla. I do not care for the filezilla layout, but both of these are free so try them out see what you like. WinSCP does have a internal text editor which can prove handy for small quick changes. The layout also does not have the two extra tree views that I dislike in filezilla.
There are several Firefox plugins available. I do not personally use them but I have heard good feedback on FireFTP, which can be found at https://addons.mozilla.org/en-US/firefox/addon/684. This plugin is supported by Firefox 3.0-3.5, so beta users can still use it fine.
If none of these seem useful give goggle a try :).
ranma wrote: Going off of what p4 said, you could even make your own client using the basic dos ftp commands. Maybe make it a little prettier :P
Well, if you were to make your own I would recommend to get a decent understanding of command line first. Would help out a bit :p. However, the time required to build a reliable ftp with common support such as drag and drop would be highly time consuming. Modding an existing FTP could prove harder as well, due to the in-familiarities of the programmers style.