putty is like ssh client for Windows (and Linux). It only supports console mode, or if there is builtin console GUI.
If you need GUI access via secure line, I would recommend NX Client/server
. GPL version supports maximum of 2 simultaneous connections (I think), and you are logging to your user account (root login is disabled by default) like you would locally, and that connection is made via SSH, so security is very high, unlike the VNC. It is important to say that when you are using NX, you are not taking over the current screen (like VNC server for Windows), every user logs in separately, with his own GUI and user settings, right, etc.
There is also freeNX project (CentOS has it as part of the distribution), but so far I found NX much better choice.