How can I make a linux distro run without a Partition like Puppy Linux, Wubi, etc.?
 

I'm just wondering what technique these OS's use. I know Wubi creates a virtual disk inside windows, to which Ubuntu is installed and run. I am assuming that Wubi mounts this disk as if it were the root partition. Puppy linux seems to do the same thing.
What do they call this and how can I make something like Slackware run like this?

It's emulation or virtualisation. Check out Qemu, VirtualBox, and VMWare.