Usually, keeping the boxes only matters for a few reasons: resale, collecting, and shipping/service. Original boxes and manuals can help resale value somewhat because some buyers like complete packaging, and this can matter more as items get older and boxes become rarer. However, for common camera bodies and lenses, condition and included accessories like caps, hoods, tripod collars, batteries, and manuals generally matter more than the box itself.

Boxes may also be worth keeping during the warranty period, since they can make packing gear for service safer and easier.

For collectors, boxes add value mainly when the item is unusual, historically interesting, or especially collectible. For ordinary consumer gear, the box often adds little.

So if you do not plan to sell, are out of warranty, and storage space matters, it is reasonable to recycle the boxes. If you want a middle ground, keep boxes only for especially collectible items or currently in-warranty gear.