I have a fairly well-stocked mini-bar, but not a lot of space. I've considered storing the bottles in a drawer, but I've heard that you should store certain alcohol upright. Is this true? If so, why? If it's only true for certain types of alcohol, which ones?
Beer bottles should be stored upright. This is to minimize contact (and hence oxidization) between the beer and bottle cap, and (for unfiltered beers) to keep any sludge on the bottom of the bottles. (How To Store Beer)
Wine should be stored (mostly) on its side. This keeps the cork moist; and a dry cork can shrink and allow too much air into the wine bottle. (Storage of wine) But note that:
The rules for liquor aren't as defined, but it should generally be stored upright. (Taming Your Liquor Cabinet). It's stored that way at the factory, and it's shipped and displayed that way. Also for many "fancy" bottle types, the bottle won't even sit properly on its side. Also, alcohol in liquor can leak through - or even break down - whatever material is used for the cap. But it's generally safe to store liquor bottles horizontally in the freezer for a time. It depends a lot on the specific bottle and cap in use.
I have to concur with KatieK as to the conclusion that liquor bottles should be stored upright, as for "Why?" While I can not necessarily tell you "the reason" I can tell you "my reasons"... Liquor bottles lids are less reliable after they have been opened, upright storage prevents leakage.
I have had the unfortunate experience with a bottle of Jack that didn't keep well.
An additional reason to do this is that in all of the bars and liquor stores I have visited, I can recall never having seen liquor stored sideways...if it made sense to store those sideways the retailers would do so.
These may not be perfect reasons, but they are good enough to me...for whatever that is worth to you.