There's currently (ArcGIS 10) no easy way to determine when a geodatabase's license expires (workgroup or enterprise) short of inspecting the GDB repository tables. It would be useful if this information was reported on the Administration tab of the geodatabase properties (this tab would need to be added to an enterprise GDB properties dialog since it's only there for workgroup GDBs at ArcGIS 10).
Since a Database Server's licence expiration date might differ from that of individual workgroup GDBs, it would also be useful if the Database Server's license expiration was visible on the Database Server's properties as well.