Carbon-zinc D cells can be usually had for low prices and have enough grunt that they can run flashlights of respectable power. I still wouldn't run a Cree on them, but, say, three medium-brightness LEDs might be doable.
Carbon-zinc AAs can be used in low drain devices such as, say, a single, non-overdriven 5mm LED light. However, they won't be terribly happy even under such a low draw, and will probably give less than half the runtime of even a cheap Alkaline. Better to use them in
clocks and remotes.
CZ AAAs shouldn't be used in anything else but clocks and remotes.
CZ 9V batteries, too, should only be used in such devices, since they have truly pitiful power and energy density.
I never actually buy CZ cells, but things I buy from DealExtreme often come with CZ cells inside them, to keep my clocks happy.