Lots of great info on this string. I'd like to make one slight "correction" to comments that DaveO and Alan made (and this is a very, very rare opportunity!).
In terms of degrade that occurs during the drying process, most drying-related degrade occurs when wood dries from green to 35%MC. HOWEVER, the degrade (that has already occured) is not revealed until the wood is below 25%.
Thus, if you see checks, warping, cupping, etc when your wood is around 20%, it isn't due to anything that happened recently, but rather much earlier during the initial stages of the drying process. (On a side note, that's one of the biggest benefits of Kiln dried wood versus air dried wood - the ability to control the rate of moisture loss while the wood is above 35%MC. This is critical for slow drying species such as oak, sycamore, or any 8/4 or thicker wood.)
If you store wood (either horizontal or verticle) and the MC% is below 25% but above 16%, be sure to leave a 3/4" to 1" gap between the boards so that you can get some airflow.
I also second the idea of putting some type of spacer between your vertically stacked boards and the floor, for the purpose of preventing moisture from wicking up through the concrete and into your boards.
I like vertically stacked boards - not only do they take up less floor space they also are much easier to pick through when selecting a specific board. Alan's photos cleary depict why.
Scott