Answer
Click Start > Programs > ArcGIS > Desktop Administrator.
In the section on the right, labeled ArcGIS Configuration, there is a listing of general information, including any applicable reference to the Service Pack. See the following listing for an example:
Product Name: ArcGIS Desktop
Version: 8.1
Product Version: 8.1.0.642
Installation Folder: C:\arcgis\arcexe81
Installed By: gisuser
Install Date: 10.24.2001
Install Image: D:\ArcGIS
Current User: gisuser
Application Data Folder: C:\Documents and Settings\gisuser\Application Data
System Temporary Folder: C:\Temp
Service Pack: 1 (build 649)
Service Pack Installer: gisuser
Service Pack Install Date: 11/09/01
Service Pack Install Time: 13:47:55
Service Pack Status: Complete