How don't I store bags, is a better question? Bear in mind that I have space limitations and ALSO many bags:
-I have some on one of those over the door things on my bedroom door. Mostly non-leather totes and backpacks.
-I have some smaller more casual ones ones on pegs in my bedroom
-I have shelves in my bedroom and closet with bags on them.
That said, I keep only a few bags in rotation at once. They stay on the knobs of my bureau drawers, which is a system I hate but I can't think of anything else to do with them.