Your bags need to be accessible and protected from damage. Shoving them into the bottom of your cupboard not only makes you forget what you have, but damages the bags. Tucking them away in hard-to-reach-places is tidy, yet impractical. On the other hand, bags are bulky and you are probably running out of accessible closet space as it is.
I ran into this problem recently but managed to find a good solution. I ordered a “handbag rack” from ImprovementsCatalog.com. The rack hooks over the top of a door. It also has a hook at the bottom that is attached to a piece of elastic so that your bags are kept in place as you open and close the door. The rack can hold up to 8 bags of just about any size and will cost $9.99. It is orderly, out of sight, accessible and visible. My handbags and I are happy.