You could also use the "tar" command to archive the multiple files into a single file. This file could then be copied to the 2nd server with the utility of your choice (e.g. FTP).
If the file is large, you may want to consider compressing it with a program like "gzip" prior to the transfer.
rcp for non-interactive use system B needs a valid IP@ or hostname for systemA in ~/.rhosts (chmod 600 ~/.rhosts), with -r recursive get/put
rexec for non-interactive use system A needs a valid entry in the ~/.netrc file with username and password (machine systemB login username password userpassword init macdef)
ftp non-recursive
ncftpget can do recurseive FTP get with -R
ncftpput FTP put, similar to ncftpget
wget can do recursive HTTP get with -r
ftpcopy can do recursive FTP
curl can do a lot of stuff
You can also mount a NFS filesystem from the other host to your local and do the traditional (in this case with Kornshell):
cd /nfsmountedfilesystem
tar cf - .|(cd /localfilesystemtocopyto&&tar xvf -)