Ok, I've got a different possibility. It's not a third-party service (all I've found look to be clones of net2ftp), but a web-based editor you could install on your own site and use from there: Webpad. I know it's still not quite what you asked, but it should fulfill the requirement of not needing to bring anything with you. It does also support opening files via FTP among other things if you wanted to install it on a separate server.
Edit: decided to have one more go at this after bobdias's comment and turned up a couple more options. The magic google turned out to be web-based source code editor. Newest to oldest:
This article about Bespin looks promising but the bespin website doesn't work for me right now.