Multiplexing of the control file is done so that if you lose one control file, you will still have others to use. What concerns me is where you said, "is it necessary to take a backup of the whole control file folder?" This implies that all of your control files are on the same disk volume. If you lose that disk volume, you lose all of your control files. It is important to multiplex your control files to multiple disk volumes, if at all possible.
That being said, backups of your control files are your defense against losing all of your control files. You only need to back up one control file, but as a practice, I back up all of them. I also perform a binary backup of my control file with the ALTER DATABASE BACKUP CONTROL FILE command. This gives me one more backup of my control files. I also perform a backup to a trace file with the ALTER DATABASE BACKUP CONTROL FILE TO TRACE. This may seem like overkill but with a file as important as the control files, I feel that all of these backups give me many more options should I need to restore the control file. And the backups are typically pretty small.
If you are using RMAN, then you can have RMAN back up the control file for you. I still perform the ALTER DATABASE BACKUP CONTROL FILE TO TRACE when using RMAN.
This was first published in January 2006