It is quite difficult to get your head around this one, Deciding what to keep and what not to.
I always keep the last Three Full Backups, the Transaction Log backups and Differential Backups between them.
Once the Full Backup is performed on Sunday night, these are restored on a Test DB on monday morning, if they fail, Back it up again.
I became complaisant with the backup routine and decided that One Full was enough after IT complained i was using too much disk space on the SAN for storing the DB backups and suggested I alter my backup routines... so I began to keep only the last full and the transaction logs after, but got seriously burned one day a few months ago when the backup on the disk were corrupted and the DB server went down on monday morning before i came in due to a hardware failure.
We live and learn, but that day in August will probably remain with me forever more...