The simple backup and recovery model uses full database backups. It requires the least administration since you don't have to administer transaction log backups and log space. However, in the simple backup and recovery model, data is recoverable only to the most recent backup. Changes made since the last database backup are lost.
How often you perform backups when using simple recovery depends on how often the data changes.
If you are using ArcSDE geodatabases for SQL Server Express created under your ArcGIS Desktop (ArcEditor or ArcInfo) or ArcGIS Engine license, only one editor can be making changes at a time. Therefore, it would be best if the editor periodically created backup files while working, just like you would periodically save any other type of file as you are working on it.
If you are using ArcSDE geodatabases for SQL Server Express licensed under ArcGIS Server Workgroup, your backup schedule should be determined by how much data you feel you can stand to lose. It would be best if you plan your backups for specific times, such as putting them on the same schedule as your operating system or file backups. If you want to do backups more frequently, try to schedule them to take place when other users won't be accessing the database, perhaps at the end of the day.
If server failure or database corruption are likely possibilities at your site or if you require point-in-time recovery and transaction log backups, you need to move to ArcSDE geodatabases licensed under ArcGIS Server Enterprise.
You should always make a backup of your database before upgrading or applying any service patches to it.