I only have a few so I use one of the "Really Useful Boxes" from Office Depot (love these things!!). It's a flat one - like 9"x12" or something, by about 3" deep, so the punches all sit in one layer and are easy to identify. When I outgrow it I'll get another box exactly the same, but it'll probably be a while because now I have my die-cut machine I don't really need many punches.
But even if I had a whole bunch of punches (sounds like the name of a band or something, lol) I would use the same system, just a whole bunch of these boxes, because my crafting space is the living room and an over-the-door hanger would simply not work. All my stuff is organized in a cabinet with doors so I can close my mess inside. The Office Depot boxes stack really well, so I'd organize the punches by shape (circlese, butterflies, whatever) and label the boxes to find what I need.
I had a couple of spice rack type shelves that I used to keep my acrylic paint bottles on before we moved. Since being here I have put my paints onto a different shelf system, so use the small shelves in my 'craft closet' to hold punches. I have a card table in the closet to work on (when the table is more empty) and then the shelves hang on 2 of the 3 walls in front and to my left as I stamd at the table. I have easy visual on what punch I need and can easily reach if nobody has piled stuff in front of the shelves. I did get the shelves for just a few $ at garage sales, painted them the color I wanted and I like them alot. Inexpensive and easy!