I know mulching when mowing is typically a good thing for the health of the yard. If this is the case, under what circumstances should I bag the clippings?
Well I'm intrigued - your statement 'mulching when mowing is generally a good thing' is not one I'd agree with, in principle. I don't know what kind of grass you're growing, but in the UK, we do not let the clippings lay on the lawn UNLESS the weather is very hot and dry, and likely to continue to be so. Allowing clippings to remain on the lawn increases the amount of thatch, blocks light from the blades of grass, may encourage weed growth if you already have weeds in the lawn, and encourages fungal diseases. They are, though, left when the weather is hot and dry as a bit of protection from the heat, and to provide a bit of much needed moisture for a brief period.
Given where you are, it's likely that your summers are much more 'summery' than ours, in which case, the 'when the weather's hot and dry, let the clippings fly' rule applies - provided the clippings are not full of weed seeds.