This discussion uses 1st Edition AD&D sources, and assumes that the various descriptions and definitions were unchanged for 2nd Edition AD&D.

Basically, all protective equipment can be categorized into two divisions which I'll call a "foundation class" and an "improvement class". The "foundation class" is composed of those protections which lend a fixed, static AC number to the wearer, which by definition cannot stack (add cumulatively) together; these include normal and magical armor and shields (PH36), bracers of defense (DMG139), the robe of the archmagi (DMG152), and the spells armor (UA52) and shield (PH68). All of these give a predefined and fixed Armor Class, and no rule is given which allows them to improve upon each other, so if several are used only the best protection is effective. (Note that the difference between the two 1st-level magic spells is that armor gives a long-duration, minimally effective protection; while shield provides a very short-duration, highly effective defense.)

The "improvement class" contains those items which give a bonus of some number of improvement points to the wearer's AC. In general, all of these magic items of protection are explicitly noted to combine cumulatively with all other such items (and, by default, with any items from the preceding class as well). These include the ring of protection (DMG131), cloak of protection (DMG141), cloak of displacement (DMG140), and boots of speed (DMG139). Note that by their nature, only one instance of any of these item types can be worn at a time; and this includes the ring of protection, which is noted to only allow a single such ring to be in effect on any one person (DMG131).

Now, there are a few other specific rules, introducing more restrictions to the general guidelines above, which I'll note here. The cloak of protection will not work with any armor or shield (with the exception of non-magical leather armor; DMG141). The ring of protection will not work with any magical armor (which must presumably include any magic shields; DMG131). The armor spell will not work with any item of protection (except for the solitary case of a ring of protection; UA52).

Finally, there are additional notes for the various items and spells which are redundant with my general guidelines above; they can be considered to simply be clarifications to prevent player confusion (such as when bracers of defense and the armor spell point out that they don't function in tandem with conventional armor).

How did these rules change between AD&D and D&D 3rd Edition? Almost not at all; the only significant change is that the shield spell, by virtue of being a "cover" bonus, now stacks with practically everything, where it formerly did not. Other than that, everything in what I identify as the "foundation class" became "armor" bonuses, and so still do not stack with each other. Meanwhile, everything in the "improvement class" was given separate bonus types, so they each still stack with all the other protections. With the exception of the significantly increased utility of the shield spell (and the removal of the trio of special-case rules, above), everything remains exactly the same with regard to armor stacking issues as it has been since 1st Edition AD&D.

To see how the armor-stacking rules work in the newer D&D 3rd Edition, see here.