I have a colleague that uses 9.2 and has access to our server in which I have multiple geodatabases that were created in 9.3. Is there any way for her to access the data?
You can access 9.3 SDE geodatabases from ArcGIS 9.2 with Service Pack 5 or higher installed. See Compatibility between clients and geodatabases.
It is a bit different if you need to use direct connect, but this case is also described in the document above.
EDIT: Also, the FAQ: How can previous versions of ArcGIS Desktop connect to geodatabases created with newer releases? document (published just recently) has some additional information.
as petr k. said SDE could work, in the case of Personal or File Geodatabases, this is not possible. It is a matter of timing. The Geodatabase model changes over time and these changes are reflected in the connections from the desktop software. If the database is a later version then the older desktop does not have the required vocabulary to speak with the newer database so even if it could work would be fraught with danger.
This can work for ArcSDE because the ArcSDE product is a much more stable and consistent product, and as such specific translators have been written for the older client to the newer database at an enterprise level
Hope this helps and is not all bad news, CDB