Every wine rack in the world holds bottles horizontally, which suggests the question is settled. It is, for cork. For the growing share of bottles that are not sealed with cork, the answer is different, and it changes what you can do with the space you have.
Cork needs contact with the wine
A cork works because it is swollen tight against the glass. Lying the bottle down keeps the cork in contact with the wine so it stays moist. Stored upright for long enough, the cork dries, shrinks, can crumble into the bottle and lets air past, which oxidizes the wine, as WSET explains in its storage notes.
The timescale matters. This is a problem measured in months and years, not days. A cork-sealed bottle standing on a kitchen counter for a two weeks before dinner is fine. The same bottle standing for three years is a gamble.
Screwcaps can stand up
A screwcap seals against the glass rim with a liner and does not need moisture to stay effective, so those bottles can be stored upright, and a large and growing share of wine is now closed this way. Upright storage is often the better use of a closet, since bottles standing in a box use less depth than a rack.
Storing a screwcap bottle on its side does no harm either, so a mixed rack needs no sorting. The freedom only matters when you are short of rack space and long on shelf space.
Humidity, and how much you actually need
The traditional cellar figure is around 70 percent relative humidity, which keeps the exposed outer end of a cork from drying. In a home collection this is far less important than temperature stability, because the wine side of the cork is doing the real work if the bottle is lying down.
Very dry air over many years is worth avoiding for long-term storage. Damp is the more common household problem, and it damages labels, boxes and cases rather than wine. If you are choosing between a stable dry closet and a damp fluctuating garage, take the closet and accept the labels will outlive the argument.
The exceptions worth knowing
Sparkling wine keeps its cork moist through pressure and a saturated headspace, so upright storage is fine and often saves space. Fortified wines closed with a stopper rather than a driven cork are usually stored upright, because prolonged contact between high-alcohol wine and cork degrades it. And any bottle with sediment should stand up for a day or two before opening so the deposit settles, which is where the decanting guide picks up.
Location: Closures stored there: cork / screwcap / mixed: Bottles lying down or upright: How long they will be there: Sparkling or fortified kept separately: Action needed:
What this means for your locations
Record which locations hold bottles flat. A case moved during a house move can easily spend a year standing upright in a corner without anyone deciding that it should, and the moving guide covers keeping locations honest through the disruption.
If you are choosing racks or reorganizing, the rack and row guide covers naming locations so that a change of position is a change you can see in the record rather than one you discover years later.