Every time I save a file on my Mac, I want it to auto-sync with the files on my remote server.
Are there any text editors that can do this?
Coda is a web developer oriented source code editor that has integrated "site" management and assists in keeping the local and remote sites synchronized by highlighting all files with local changes and providing easy means to upload changed files.
It supports SFTP (SSH File Transfer Protocol) for file transfer, and has some SSH capabilities (which I haven't used so far, though).
The TextMate 2 alpha was just released, and it has something similar to what you want:
rmate. So if you log into SSH (not SFTP/SCP), you can run that script and edit the files locally using TextMate.
Maybe not exactly what you want, but if you use Cyberduck you can actually edit the file remotely by right clicking and selecting Edit with... and it will be uploaded automatically each time you save.
Cyberduck also has the option to synchronize a folder on demand (Right click → Synchronize) in case you need that.
TextWrangler for OS X is free, fast, and highly functional. It includes native capabilities to modify files via SFTP/SSH connections.