What's your rule-of-thumb for rotating stored water supplies, that is, how often do you dump the old and refill with new? Does the storage system used have an effect on timing?

I'm a south Florida resident so my timing is geared to hurricane season. I used to write the year on gallon jugs and try to rotate from there. I finally simplified my life by buying about 40 OR 50 gallons (for a family of 4)in May just before the season. Then we just drink the stuff after the season and restock again in May. Not the most economical approach but it makes one more aspect of hurricane season simpler.
Also, having kids who are notorious for taking two sips out of a large jug of water and then disavowing any knowledge of ownership, I switched to only half liter bottles (store brand of course to save bucks). When someone gets a bottle they put their initial on it and they don't get a new bottle until I get an empty with their initial. It may sound a bit draconian, but you'd be surprised how much longer the water lasts - and they get into the habit pretty quickly any how.

Every June and December, I swap my water out.

Every six months for us too.

I bought a couple of 4L water bottles and just follow the expiration date which is about 2 or 3 years. For water meant for cleaning, I fill empty 3.6L bleach bottles of tap water. In theory, if your water containers are sealed and away from light it can withstand easily many variations in temperature and stay drinkable almost indefinitely. But just to be sure, generally it is recommended to rotate stored tap water every six month.

Frankie

I buy 4-packs of 2-litre bottles from a supermarket. They have an expiration date of a year or two and I am happy to keep them a few months beyond that. I also buy smaller bottles which I find convenient for camping and they mostly get used with a year.

I also have a fish aquarium with about 160 litres in it which gets changed to suit the fish. It gets refilled from a 40-litre tank and you have to tap water to stand for a day before giving it to the fish, so I try to keep it full all the time.

I don't bother with storing tap water otherwise, because I don't think it's worth the uncertainty about expiration nor the effort of replacing it frequently enough to be safe.

I will drink my 4L bottles and replace it with smaller bottles because it's more convenient for bug-out situations.

I buy mineral water in 5liter bottles.
I have about 12 such bottles in my cellar.
When I have drunk 2 ou 3 bottles, I replace them.
I recently (last month) started to stock bleached tap water, using the 5 liter empties, to have an extra stock on hand, if need arises (using this water not for drinking but for other usage : washing (self and/or dishes), toilet flushing etc...) Clutter considerations will limit this stock to another 12 bottles. If I can make more room in my cellar, I plan to stock more bottles.

I intend to rotate this bleached water every 6 months/1 year (not sure which, yet).I won't drink it except to test if it's still OK, but will use it to flush the toilet (I don't want to waste water)

I replace my non-storebought stuff around June 1st and again around October 1st. I figure the heat is a lot harder on it than the cold. Seems to work well so far.