The short answer
Vertical storage — boxes standing on their spines like books — is the better default for most collections, and it's the louder camp in every discussion of the topic. It uses shelf height efficiently, lets you pull any game without unburying a stack, and, counter to intuition, stresses boxes less than stacking them, because the real damage comes from weight pressing down, not from orientation. People who switch from flat stacks to spine-out routinely report their boxes ending up in noticeably better shape. The one real catch is that upright storage demands organized components. Horizontal (flat) storage is the safer choice for specific exceptions: oversized boxes, games with heavy unsecured bits, and damaged or bulging boxes.

When vertical wins
Standing boxes upright is the right call for the bulk of a collection.
- Standard-size boxes with organized or tightly packed components — they stand fine and stay readable.
- Games with good inserts (Isle of Cats, Wingspan, Century: Spice Road) — nothing shifts when they're on end.
- Medium and large collections — vertical uses full shelf height, fitting far more games.
- Display shelving — spines out reads as tidy and lets you browse the collection at a glance.

When horizontal is safer
Flat storage still has its place for the exceptions.
- Games with loose trays or lots of small bits (Great Western Trail, Survive: Escape from Atlantis) that would dump to one side standing up.
- Big-box and oversized games that don't fit a shelf upright without overhanging.
- Boxes that are bulging, damaged, or have weak lids that won't bear a neighbor's weight.
- The top few of a stack only — never deep stacks, which crush the bottom boxes.

Box creep, and how to stop it
The main knock on vertical storage is box creep: lids that slowly lift and components that shift toward the bottom edge. It's real, but hobbyists agree it's largely solved. The most-recommended fix is a box band — an elastic or silicone rubber band stretched around the box (silicone lasts, since plain rubber degrades over time) to hold the lid shut in transport and on the shelf. Beyond bands, the standard tricks are to bag components in ziplocs, use an insert that comes flush to the lid, keep the empty punchboard frames and lay them on top to fill the gap, pack heavier components toward the side that becomes the bottom, and store games snugly so neighboring boxes hold each other's lids closed.

Orientation is per-game, not per-collection
The nuance most people settle on is that orientation should be decided game by game. Titles with great inserts or tightly packed trays store vertically with zero issues; titles with loose lidded trays or a pile of small tokens spill if tipped and are better off flat. There's no rule that a whole shelf has to match — plenty of people run a deliberate mix, standing the well-organized games and laying the messy ones flat, and that's the sensible outcome rather than a compromise.
The real enemy is stacking, not standing
The strongest argument against flat storage, repeated over and over, is that a tall stack dishes and dents the box on the bottom — worse when the stacked boxes are mismatched sizes, so the weight lands on the weak center of a lid rather than its edges. If you do stack, keep piles shallow, three or four boxes at most, and size-matched with the heaviest on the bottom. And once a collection gets big enough, the whole debate goes out the window: 'if it fits, it sits,' and box-Tetris wins.