Definitely horizontal. Sometimes I feel like the only one who can't use the fruit and vegetable bins in the fridge because I immediately forget about anything I've put in there, and it rots.
However, like other commenters, I wonder if it's less an issue of horizontal versus vertical, and more a matter of "out of sight, out of mind". If I can't physically see something, I have a very hard time remembering it's there. Thus, storage systems like drawers, filing cabinets, and to some extent cupboards are pretty ineffective for me. Shelves and table tops are much better, and see-through closed storage devices are somewhere in between.
However, like other commenters, I wonder if it's less an issue of horizontal versus vertical, and more a matter of "out of sight, out of mind". If I can't physically see something, I have a very hard time remembering it's there. Thus, storage systems like drawers, filing cabinets, and to some extent cupboards are pretty ineffective for me. Shelves and table tops are much better, and see-through closed storage devices are somewhere in between.