A well-maintained geodatabase is a performant geodatabase. Database maintenance requirements vary from system to system, but there are several routine tasks that need to be carried out on all systems.
Although not necessary for performance, database backups taken on a routine schedule are crucial to the safety, integrity, and security of your system. Not only do database backups protect you from data loss in the event of system failure, they also protect you in the case of data corruption. Database backups are typically scheduled and handled by the database administrator, but it should also be the responsibility of the geodatabase administrator to ensure that this process is in place and carried through.
Just as important as taking the backups, is to routinely, yet randomly, test your database backups. This entails restoring backups to a different SQL Server instance to ensure that the backups are valid and current. This also keeps the staff current on the protocols...