I use CFFile to upload files all the time on the same server Cold Fusion 8 is located on.
Now I want to use CFFile to upload files on another server.
Everytime I put in the destination directory for another server it fails saying it does not exist.
For example here is how I call the destination (on another server) directory: \\\\\otherServer\directoryOne
I also tried playing with slashes and adding http:\\ and nothing works.

Is there something in CF Admin that blocks access to another server when using CFFile?

I have not done it in a while, but the other server has to be accessible to the account CF is running under. For example, if the other server is set up as a mapped drive, the ColdFusion user account must have permission to access that drive. IIRC, the typical user account "System" (on windows), does not.

In other words, cffile only works on your local server (or any drives accessible on your local server).