Down sleeping bags and down jackets should not be stored in the stuffbag, but as loose as possible. Tents, as far as I know, can be stored stuffed as long as they are dry. Are there any other materials or equipment that I should be aware of that should not be stored in the same bag as when I'm carrying it on my backpack?
Thermarest and other self inflating foams should be stored inflated, not deflated and rolled up. Generally anything that has a small form and a large form, and is expected to transform into the large form on its own should be stored in its large form. (So an air mattress you inflate can be stored in the small form, but your sleeping bag and pillow shouldn't be compressed.) I have some ordinary open cell foam pads as well and they're best stored flat or they develop a curve.
Nothing should be put away wet or dirty.
Electric cables shouldn't be tightly wrapped, especially around hard things like a power brick, but should be just loosely coiled. That may mean they can't fit in the bag you carry them in on a trip.
Bungees or elastic straps should be stored with no tension in them. Just let them hang loose. I guess the general version is if it's supposed to transform into the small form on its own, store it in the small form.
If you'd broaden "down" and "wet tents" categories to "all insulators" and "all wet items", it'll cover pretty everything, I think.
Also a membrane jacket might stick to itself (coalesce) and may get damaged when you unstick it (membrane layer may peel of).
One could think about rubber, which takes new shape under prolonged pressure, but it's not what you are usually carrying in your backpack. Thin metal parts like tent poles are potentially subject to this effect, but I'm not sure it actually happens.