I want to install Debian Unstable alongside Maverick but I don't want to lose my data.
Also my CD drive is Broken.
Installing Debian without a CD drive
If you have the partition space to install Debian along side Ubuntu as a dual boot setup (as mentioned in previous answers), then as you have a broken CD drive you can install Debian (and other Linux distributions) from a USB memory stick.
Using the System > Administration Startup Disk Creator you can create a USB memory stick from any of the Ubuntu CD images, the .iso files. You may be also able to use debian .iso files with the same startup disk creator.
Alternatively, you can use unetbootin which will create live and install USB sticks from a wide range of distributions (it will even download the the .iso files for you for some distributions).
Installation from a USB memory stick is exactly the same as from a CD, however for some PC hardware when first switching on the PC you may need to press the escape key when you see the manufacturers logo to bring up a boot menu allowing you to select the USB memory stick as the boot device.
If you have an existing Ubuntu installation and a decent network on your side, you can use
The normal process would be to reparition your HD (if you don't have another one), install Debian into the new free space, don't install a new grub, edit Ubuntu's grub to boot to Debian and you're done.
However, I've just found Lubi which gets its name from Wubi. It basically allow you to install a linux to a file in your existing filesystem and then just loopback-mount it and chainload into it from Grub. I've made it sound more complicated than it is... But it looks like it should work.
It certainly seems a lot less destructive than repartitioning could be.