For accessing files from an FTP server, you'll have to use a proxy. I've been meaning to write one of these myself, but I've not had an opportunity to do so. Here's how it would be laid out:

1) External HTTP-FTP or SOAP-FTP proxy waits for Apex Code to connect and request a file.

2) Apex Code calls request to the proxy.

3) Proxy calls the FTP and retrieves the file.

4) Proxy returns the file via HTTP back to Apex Code.

5) Process the data as normal in Apex Code.

For sending files to an external server, you can basically do anything you could do with a normal HTTP or SOAP connection. For example, you could set up a form on a server, and have it accept a POST from salesforce.com, and submit that data to the external file server. You could also use a web service that was designed to accept connections and forward them to FTP servers. You can also use salesforce.com's email messaging capabilities to craft an email that could be sent to a server somewhere; the server could pick off the attachments and store them on a server.

In short, there are a ton of different options available. I'll see if I can't craft a FTP proxy, it looks like it should be deadly simple using PHP. I've bookmarked this post so I don't lose it; if I come up with something, I'll let you know.

In the meantime, let me know if there's anything I can do to help point you in the right direction. File access is fairly trivial once everything is in place.

P.S. Thanks for the vote of confidence!