GLee,
That is a reasonable question. Although Database Mirroring and Log Shipping independently are good high availability\disaster recovery techniques, they should not replace full backups. Full backups can be considered the last line of defense in order to prevent a catastrophic issue.
As a point of reference, in the same database are you performing both Database Mirroring and Log Shipping? If so, why are both of these processes needed in the same database. Is Database Mirroring used with SQL Server 2005 instances and is Log Shipping used with SQL Server 2000 instances?
For the Log Shipping databases, full backups are needed to start the process, so it might make sense to issue full backups on a daily or weekly basis. With SQL Server 2005 you also have the ability to issue COPY ONLY backups, which might be a good alternative to obtain your full backups while not having to ship a large full backup. Here is a tip on COPY ONLY backups - http://www.mssqltips.com/tip.asp?tip=1075.
For the Database Mirroring databases, full backups should be issued on a daily or weekly basis depending on rate of data change and the acceptable amount of data that can be lost.
If you have an environment where the data rate change is very low (weekly or monthly data uploads), then backups may not be needed as often. That decision is based on the acceptable amount of data loss and the volatility of the data.
Another key item here that typically gets left off is the need to recover. Take a look at your high availability/disaster recovery plan and make sure it will cover all reasonable issues if you had to bring the systems back up and running. Also consider the steps someone else on your team (or external to your team) would have to take if a major issue occurred.
For more backup and recovery tips, I would recommend checking out these tips:
Thank you,
The MSSQLTips.com Team