Dropbox has the unpleasant property that it doesn't let you put its repository on a network drive. But it does work, albeit with some effort. Whether the effort pays off may be decided by everyone alone: repository in the roaming profile (default) results in long login and logout times (every time), putting the repository on the H: drive takes quite a while (once, because it is completely downloaded from dropbox once).

For the lines starting with "cmd:" you need a shell. This is what you get as follows:
  start → "cmd(enter)"
In the resulting window you can then enter the commands below, everything that is behind "cmd:".

The manual:

•     Download the Dropbox-Installer, save it to c:\users\<username> (make sure you go there!)
•     Close all windows. ABSOLUTELY. Windows Explorer may remain open for c:\users\<username>
•     cmd: net use h: /d
•     if query: Yes
•     cmd: mkdir c:\users\<username>\dingsda
•     cmd: subst h: c:\users\<username>\dingsda
•     Start Dropbox Installer (not all necessary entries are detailed here):
•         install without admin rights: "Current user
•         log in to dropbox
•         Advanced settings → Set repository ("location") to "H:".
•         "Open my dropbox folder"
•     Wait until Dropbox is synchronized.
•     End Dropbox. (Not only the window, also in the taskbar!)
•     cmd: subst h: /d
•     cmd: not use h: \\\psi\<username>
•     cmd: xcopy /e /q c:\users\<username>\dingsda\dropbox h:\dropbox
•     cmd: rmdir /s /q c:\users\<username>\dingsda
•     Restart the Dropbox (Start menu). Now everything should work. Also other programs again :-)
•     Optionally create a link in the start menu under "startup" that starts Dropbox at every login.