As per my experience I would say that I can use my desktop which is hosting windows XP operating system without a mouse.
Few years earlier my computer had a problem with my general mouse pin. The pin got damaged and it did not use to recognize any of the mouse attached to it. The same mouse used to work on other systems.
Being lazy to call a hardware professional I got to know of the option where keyboard can be replaced by mouse.
Using the numeric key pad on your keyboard you can navigate the mouse pointer as you would with a mouse. Though it took some time for me to get used to it it proved to be useful as within days I got used to working on the computer just with the help of keyboard numeric key pad navigator and some general key board shortcuts.
It is very difficult to imagine a computer without a mouse. But in olden days, there was no mouse for desktop computers. I really wonder how they were using their computers without a mouse. Mouse is very important pointing device in a computer.