All of this seems to fall under the general principle of "eliminate before you optimize", but it's good to have reminders of specific applications every once in a while.
editor: vim
FTP: FileZilla
file management: combo of VCS rsync
Editor: Substitute your favorite lightweight, powerful editor for vim. Emacs and textmate are good choices, I hear. I stuck with vim and am quite happy, because using the mouse or arrow keys feels like so much effort. I don't like the heavy meta key dependence of Emacs: most of the people I know who use Emacs have special keyboards, whereas I'm very comfortable using my notebook keyboard for vim. Haven't tried Textmate because I run Ubuntu, but Mac people give it a lot of praise.
FTP: I actually use FTP very sparingly, mostly for clients that have no idea what a VCS is, or have FTP-only access to their server. If I just need to upload miscellaneous files, like images etc., I'll scp or rsync from a shell. But FileZilla is pretty good, and it's cross-platform.
File Management: rsync for very large files (media stuff), giant tarballs, or stuff I don't like to keep in the VCS, like config files with secrets. Otherwise, I use whatever VCS is appropriate for the project, which is usually Subversion. I use Git when I have a choice.