The Ubuntu server
When you write that you do not want to install anything in the Ubuntu server, I guess you mean except an SSH server, which you have already (for example openssh-server) or a Samba server according to this link and links from it,
help.ubuntu.com/community/Samba
If you want to log in and run application programs remotely, you can do it via
ssh user@ip-address
or if you want to run GUI application programs remotely,
ssh -X user@ip-address
if you have some basic X software installed in the server, for example
sudo apt-get install fluxbox xinit xterm
and the software you want to run.
From Windows
If you do not want to install anything into Windows, Samba is a good alternative. You can use Explorer and connect to the Samba share like you would connect to a shared directory in another Windows system via the network.
But there are several tools, that can be installed, and that communicate via ssh, not only Filezilla, but also WinSCP. You can also install an SSH client and log in.
From Ubuntu Desktop
If you do not want to install anything into an Ubuntu Desktop system, Nautilus is a good alternative. It can connect via ssh, enter the address into the box for directory to be displayed, for example sftp://sudodus@192.168.0.2/home/sudodus and you can save it as a bookmark for easy access later.
And as described earlier, you can run
ssh -X user@ip-address