I am running Ubuntu 12.04 - 32-bit. I have installed many packages that I use frequently.

How do I make a live-CD backup of my current system?

If my harddrive crashes, I want to be able to replace the drive, then boot with the CD/DVD and install to get my system restored.

I also have another system running Ubuntu 13.04 - 64-bit to which I have added many programs. I need to do the same with this system.

Remastersys is designed specifically to do this. It is no longer being developed as it was done by one person and he apparently got tired of all the whining and demands. I used it on 12.04, so you could give it a try.

You could also do it from another Ubuntu type system, something that has grubmkrescue. First install the ubiquity-installer to the partition you have Ubuntu on that you want to remaster. Then from another Ubuntu install or from a Live CD/DVD with grubmkrescue, mount your installed Ubuntu partition and run sudo grub-mkrescue. You should check the Ubuntu forums for the exact command for your release as it has been changed several times. It should then create an iso image you can burn to a CD/DVD and boot and reinstall with it. There are numerous tutorials on the Ubuntu forums about using grubmkrescue, probably some here if you use the Search function.