Standing up. If you lay them on the side and stack them the sidewalls get pushed down and it will be hard to get them back on a rim. If its tires and wheels already mounted thenit makes no difference.
I just pulled the rack out of a shelving unit that I wasn't using all that much, due to it's location. They hold up fine, even with wheels, and the tires aren't in the way at all.
Not really what's being discussed, but it works so well if you've got this kind of shelving I figured I'd toss it in here.
Cheers,
Kennith