scp host:/path/to/file .
rcp host:/path/to/file .
lynx -dump http://url > file
[download]

I think one of the modules I installed added 'GET' and 'POST' aliases in /usr/local/bin which allow interacting with a HTTP server.
At the end of the day though, it is not possible unless there's _some_ form of server app on the remote host.
What it is will depend primarily on what platform/resources you have available.