Generating Backups of Databases I would like to create a backup of four databases on one SQL Server 2000 instance at the exact same moment in time. 

How can I achieve it?

Creating different jobs with the same schedule date and time does apparently produces a difference in the moment when the backup is taken.
You will need to have the Full Recovery Model enabled on all four databases.

Now you will issue a full backup on all four databases, let's say ten minutes before the point in time you require.

Now you will do a transaction log backup of each database, at a point in time immediately after the exact moment you need.

On the other end, you will restore each full backup WITH NORECOVERY, and then transaction log backup, with the RESTORE LOG WITH STOPAT switch to specify the exact moment in time you need, as a DATETIME.

Remember to RESTORE WITH RECOVERY at the end to bring them into active use.