This is a personal preference. However, I store without the rings for a few different reasons. First, the rings should be removed after the jars have fully cooled for at least 12 hours to fully check the seal. Second, I store without the rings because sometimes a jar may lose its seal while being stored. If the ring is on, the lid may have a false seal and appear to still be sealed. And finally, the rings can become rusty if left on the jars while stored.