Is ArcGIS 10 for Desktop, ArcSDE 10 for Windows, and/or ArcGIS Server 10 for Enterprise compatible with Windows Server 2012 OS? Or do we have to install 10.1 on Windows Server 2012?
Officially : ArcGIS 10.0 not supports Windows Server 2012.
Please check out details at here
If you have ArcGIS suit 10.0 then you have chance to update the latest version i.e. 10.1 SP1 (usually its depend on licensing and its possible to update version 10.1 just confirm with your account manager)
System requirements for ArcGIS Desktop & ArcGIS Server 10.1
The new version has few enhancement and bug fixes (Please check whats new in 10.1)
thanks...please let us know if you have any questions..