I think surprisingly little, with one caveat. I used to have very little in my wardrobe. As a high schooler, I got 1/3 of a closet rack and 1 dresser drawer to share with my sisters and keep all my things. When I got to college, all my clothes still fit into just one cardboard box. I remember getting by just fine. I just had to have enough undies and things so that I don't have to do laundry all the time, but then all was well.
But I think part of the reason that it worked then was because my life was fairly routine. School, then home. Nowadays, I need a bit more range in my closet to meet a few additional social situations, so that translates into more clothes. But not really that much more.
So that is to say, a person does not need a lot. Enough to fit her lifestyle. This is the ideal. But in practice, I deluded myself into thinking that more clothes would mean more preparedness. That's true to some extent, but at some point it just became more.