Question: I had originally Windows installed on my system.Then I parititioned my C: drive and installed Ubuntu 14.04. I want o upgrade Ubuntu 14.04 to 16.04. While backing up files in the Ubuntu, should I also backup files on my Windows drives which are mounted on Ubuntu.

Answer: 
Using Ubuntu's release-upgrade feature will not touch unmounted drives. It also won't touch your Windows install on mounted drives. It won't delete your data stored in your /home directory. It often won't touch data stored in other places.

A backup of Windows files is not necessary...when everything works as expected.

We don't know your setup, or what customizations you have made that might prevent a release-upgrade from working as expected. In that rare case, a reinstall might be necessary. A reinstall DOES risk overwriting your Windows system if you mistakenly select the wrong option. Humans make lots of mistakes. Note that this is not a single-failure, but a chain-of-failures that results in data loss and a very bad day.

This is why we generally recommend a full backup of all storage before upgrading any OS on the machine. Ask yourself: "If my data were lost by one of these unlikely errors or mistakes, *how much time and/or money would I be willing to expend to restore it?*" Whatever that amount is, a backup is likely much cheaper.
Doing a full backup is a good idea, upgrading to ubunu 16.04 or even 18.04 won't remove your data from NTFS drives, you also can unmount them using umount command. linux recognizes windows files and boot by default and doesn't destroy them.
you can always check for automounted drives in the fstab file 
- /etc/fstab

[How to make partitions mount at startup?](https://askubuntu.com/questions/164926/how-to-make-partitions-mount-at-startup)