Are you planning to do the debugging itself on the server, or just host a project there? If you're only going to host your project on the server, you could setup e.g. a version control server (Subversion, Mercurial, Git) on the server, and use an Eclipse plugin for that particular version control system to sync against the server. That way, you can do all your development and debugging locally on your Windows machine, and just commit the improvements to the server from inside Eclipse.
If you for some reason don't want to use a version control system, you could configure the server to offer access to its files through e.g. a network file system (NFS, SMB ) or file server (FTP, SFTP), which you can then mount on your Windows machine and work against.
You could also install a GUI on the server, and invoke the program over the network using a remote desktop protocol (VNC should work, SSH with X forwarding might work, but I'm not sure if PuTTY supports it). I personally find the above alternatives preferable to this option though.
If you're willing to use console applications (e.g. Vim or Emacs with GDB ) instead of Eclipse, it is also possible to open a terminal session on the server using PuTTY and work from there.