You must uninstall a previous version of ArcGIS software before installing a new one. In fact, the install programs will require it. In addition, I suggest that if you have any Esri or 3rd party tools that you uninstall them first, before uninstalling ArcGIS 9.3.
A related question was asked earlier, How do I cleanly uninstall ArcGIS 9.3.1 extensions after ArcGIS 9.3.1 is uninstalled?
ArcGIS 10's default installation location is different from 9.3.1, so that helps minimize some possible conflicts. Here are the steps that I would follow:
- Uninstall any tools.
- Uninstall any SDK or ArcGIS extensions.
- If you have ArcInfo workstation intalled, and plan to install ArcInfo workstation 10, uninstall it.
- Uninstall ArcGIS Desktop.
You also might want to look through the ArcGIS installation forum.
Std Disclaimer: I am an Esri employee, but not on the install team.