This is pretty old, but the accepted answer is a bit too strict - multiple files are not necessarily a single argument to rsync. From man rsync
:
ADVANCED USAGE
The syntax for requesting multiple files from a remote host is done by specifying additional remote-host args in the same style as the first, or with the hostname omitted. For
instance, all these work:
rsync -av host:file1 :file2 host:file{3,4} /dest/
rsync -av host::modname/file{1,2} host::modname/file3 /dest/
rsync -av host::modname/file1 ::modname/file{3,4}
so OP's command would be
rsync -Pav -e 'ssh -i sshkey' user@remotemachine:/home/user/file1.zip :/home/user/file2.zip :/home/user/file3.zip .
This is not possible for older versions of rsync, but I think all major distros some with this for several years now.