Is it better to store wood vertically or horizontally? What are the pros and cons associated with both methods?
Is it better to store wood vertically or horizontally?
It depends a bit on the status of the wood when you store it, but generally it's better to store wood horizontally.
When storing wood, you have to consider three of the major forces at work: moisture, heat, and gravity.
The moisture content of wood is ever-changing, generally starting from an oversaturated state when freshly-cut to a "dry" state when the wood reaches equilibrium with the ambient air. This is influenced a lot by heat. Warm air can absorb a lot more moisture than cold air (this is why winter air feels dry, even at almost 100% humidity, but 100% humid warm air feels like walking through a swimming pool).
When you store wood, you leave it subject to these first two forces, which are always at play (unless you live in a magical world with constant heat and humidity). When initially drying wood, the third force, gravity, really comes into play.
Stacking and stickering wood is widely recognized as the best means of seasoning wood. You'll notice in the image below that the wood is horizontal, with evenly-spaced stickers separating the layers of lumber. These provide airflow between the layers for even drying. The stickers are all placed at the same location at each elevation of the stack so that the weight of the lumber is transferred directly down the stack to the supports. This reduces the bending in the wood, which means it comes out straighter when finally dry.
Wood is much more pliable when wet, thus this sort of stacking scheme is crucial when drying lumber. Once you dry a board in a deformed shape, it's hard to get it back to straight.
If you stack boards vertically, they have a tendency to bow or sag, simply due to the weight of the board. Again, during the initial drying, this can be downright disastrous.
Once you get wood nice and dry (seasoned), it makes less of a difference how you stack it (horizontal vs. vertical). Most hardwood dealers I've been to arrange their stacks vertically since it's easier to pick through the boards, though they usually have pretty quick turnaround on their stock. At home, I usually stack boards however is more convenient for the space since I generally work with kiln-dried lumber. However, most wood I buy is 3/4 or thicker, so bowing isn't usually an issue in the short term. For long-term storage, horizontal is the way that I go.
Assuming you're working with seasoned lumber, I expect that unless you plan on storing the boards for a long period or time or the boards are thin (less than 1/2", say), it shouldn't make too much of a difference whether you store them horizontally or vertically. Thinner boards I would tend to stack horizontally, but thicker slabs will be fine stored vertically.
I think the answer to this is actually both in terms of real-world applications; the ideal is to store all wood and wood products flat, but that's not always possible. And sometimes it's not needed — smaller off-cuts can safely be stored standing upright, as there's little or no risk of them bowing under their own weight.
Solid wood in plank form can generally be stored flat relatively easily because these days with modern lumber we're at worst dealing with long pieces, rarely with anything very wide. So various wall racks and even common shelving works well for boards both short and long.
Manmade sheet materials like MDF and ply often have to, by necessity, be stored vertically. Ideally they should be stored flat too, but often it's not practical for the home woodworker because we simply don't have the room. If stored carefully though the potential for sheet goods to bow is minimised; the goals are to try to have the sheets/offcuts supported along their length (rather than the top edge and the bottom edge being the sole points of contact), and for the long dimension to be horizontal, not vertical.
These factors combine to drive the design of most shop storage solutions: