What programs are mandatory for my computer?

Question

List all the programs that I must have on my computer for proper running (I am trying to delete everything on my computer (except for what I need))

Answer 1

Operating system (Windows, Linux, OS/2, Unix, whatever)

After that, a lot depends on what you call proper running. If you want to surf the internet, you need a browser (IE, Firefox,Mozilla, etc) and antivirus software.
Throw in some antispyware software while you are at it.

Ater that, whatever software that you need to do whatever you do with the computer.

Answer 2

Only the drivers for each of your individual devices (for instance, display drivers for your graphics card, device drivers for your motherboard), and even those aren't mandatory, but your computer will run a LOT better with them. (this is assuming you are using the uninstall programs utilities, and are not manually deleting system files and other hidden files from your hard drive)