At the university we had a client server based system under Windows, if I had saved a file to the 'Desktop' or to the 'My Documents' than it doesn't matter where did I log in I had this files. We would like to establish the same system in our institute. Is this possible to do with Ubuntu, or just Windows? What kind of server do I need? Is it easy to set up such a system?
NFS home folders, as suggested in the comments, clearly are a good answer. But, NFS can be a pain if your network setup is not 'static enough', for example when working with laptops etc. As the directory is accessed remotely (as supposed to 'synchronized', as in windows domains), it means that you have no access to your home directory when a network outage happens.
Samba/CIFS (see http://www.samba.org/) provides easy shared folders, and is quite tolerant to network outages. Again, files are accessed remotely, and are not available when not connected.
I personally use