Some bags like the spike that are susceptible to dents since it's lambskin may require a box, or at least not stacked on bottom of a tower of heavier bags (exaggeration). However, I dont have space for boxes either so I just keep my more delicate bags in their dust bag, preferably not leaning or touching anything else. Now that I think about it, I only do this for my spike bags. All my other bags I pretty much lean and stack next to or on top of each other.
You may consider getting one of those acrylic dividers that they sell at container stores or home goods. That way they're nicely separated. Could use for clutches too depending on how small the spacing is.