Among the most powerful of the magic items one can find is the magic ring. These legendary magic items are inspired by Norse and Germanic legends, and also inspired Tolkien to make the most legendary ring, the One Ring, which is the star of the Lord of the Rings trilogy. On the surface, rings are seen as just some magic jewelry, but their utility and use by any character class or race make them very potent. They are, however, notoriously difficult to identify and generally speaking they are generic and unadorned.
All magic rings will normally radiate magic, but they all look the same, so determination of a ring's power must be done by experimentation or trial and error. The ring must be properly worn on a finger to use. This process tends to drive players and DMs alike insane, as the item is useless unless the players are willing to play along, and the DM can keep the secret only so long before nearly bursting at the seams. Rings do not radiate good or evil (unlike the One Ring in Tolkien's saga, which would probably radiate evil as it possessed a portion of Sauron's immortal spirit). No more than two rings can be worn at any given time, and no more than one per hand. If more than two are worn, then none will function (consider this to be sort of a magical short circuit), and if two or more are worn on the same hand, the same result occurs. Rings worn in any other fashion (on toes, as earrings, or even as nose rings) do not function as magic rings. This is important to know, since I remember that at least one older module had a minotaur with a magic nose ring...
Rings function as one of the highest level powers in the game, operating their functions as if cast by a 12th level spell caster, unless the powers require a higher level of magic use. These powers would thus operate at the lowest caster level necessary to cast the spell/ability in question. For instance, a ring of three wishes utilizes the wish spell which is a 9th level magic-user spell. In order to cast a 9th level magic-user spell, a spell caster must be at least 18th level, so these functions of the ring operate as if they were cast by an 18th level spell caster (for determining if dispel magic and the like functions).
Magic rings, as stated earlier, can be used by all character classes, humans, demi-humans, and humanoids of all sorts. They can also be worn by monsters with digits who may actually benefit from their magical powers. An example of this is a troll wearing a ring of vampiric regeneration which will regenerate from its normal natural ability and also regain hit points from strikes made on targets. The caveat to this rule is that rings worn by gnomes, dwarves, and halflings have a 20% chance per use of malfunctioning due to their magic resistance. Such malfunctions cause the ring not to work. This also applies to cursed rings, so these can be removed if the ring fails to work, and the wearer is provided a hint of something being wrong with the ring (a cool way to bypass an otherwise sticky gotcha moment).
Some rings are so powerful that they are marked as such and the DM can modify these rings to reduce their potency by changing them. Such changes might include a reduction in range to touch (presumably with the hand wearing the ring), or providing only a limited number of charges before becoming useless. These rings include djinni summoning, human influence, mammal control, multiple wishes, telekinesis, three wishes, and the ring of wizardry (which is the only ring with a class restriction; usable by magic-users only).
There are only three cursed rings - contrariness, delusion, and weakness. As far as magic items go, that's pretty good odds against finding a cursed ring, until you realize that combined they make up a full 20% of the listings for random treasure rolls (yikes!). Yep, that means 1 out of every 5 rings should be cursed! Worse, these rings also function as a normal ring type of another sort, so the curse is not immediately recognized if role-played correctly. Most cursed rings require a remove curse to be rid of them. Only the ring of delusion can be removed at any time, but its comical curse is to have the player play along with the delusion, and few characters would willingly remove a magic ring if forced to by their companions when it is "obviously" working correctly.
The rest of the useful magic rings can do some pretty potent things. There are rings attuned to the elements (and corresponding elementals), some can protect you from falling or fire, allow you to move freely under hindering magic or circumstances, turn you invisible, protect you from physical attacks or spells, allow you to regenerate from death or catastrophic injury, store spells for later use (any class), reflect spells back to their caster, swim like a fish, stay warm in bitter cold conditions, walk on water, or see through solid objects. And these aren't even the most potent rings which can summon a djinni servant when desired, charm humans/humanoids at will, control mammals at will, cast multiple wishes, move things with your mind, or double a level (or levels) of spells for a magic-user. Of course, all of these powers can only be used once per round, and using them is the only thing a character should be able to do except maybe move or speak. Some require attention or concentration on the task at hand, so using the ring is all the character can do. Most rings are simply worn for the effect they provide, and it is continuous without activation (such as a ring of protection or fire resistance). Others require command words or mental activation. Some rings come with severe drawbacks if used too frequently - for instance, overuse of a ring of x-ray vision temporarily reduces the user's Constitution score (and thus might start to affect total hit points)! Many rings have only one power; some have multiple powers. Others sound like spells cast upon the person, but may also have some non-spell effect that works in conjunction with the spell-like effect. In any case, rings are very powerful and should be respected as such.
Creation of a magic ring should only be performed by the highest levels of spellcasters. Obviously enchant an item and permanency come into play here, along with the magic spells and abilities that one would normally imbue into the item. Few rings are clerical in nature, with the exceptions perhaps of the ring of regeneration and ring of free action which are both cleric spells, and perhaps a ring of mammal control since that deals with non-magical animals (which is clerical or druidic in nature). All other ring types are more or less permanent magical spells held in a ring. But don't believe that rings are trivial to make - most have several functions or spell abilities built in, and any DM worth his salt is going to make it very difficult to make a ring when you should be questing for such power in a deep dungeon or dragon's lair. Remember all the trouble Bilbo went through to get the One Ring....
The UNEARTHED ARCANA had a number of additional rings, including some that seemed just strange, unnecessary, or just weirdly specific. These new rings allowed their users to cast animal friendship on normal animals, duplicate specific functions of other rings, blink, blend into the background like a chameleon (or robe of blending), give one the non-magical powers of an elf, jump, shield your mind from spells and psionics, batter down obstacles with a ram-like force, cast shocking grasp up to 3 times per turn, sustain a person without nourishment or liquids, and reveal and prevent all lies in its presence. One additional cursed ring appears in the form of a ring of clumsiness, which disguises itself as a different type of ring and can be destroyed with a dispel magic spell. The ring of Boccob is a unique ring that does not detect as magic, and whose nature only reveals itself when some magical device contacts the wearer. Contact will prevent the magic item from working and may reduce it to a non-magical item permanently unless it makes a saving throw! This ring even has the power to affect artifacts and relics!
Rings that exist in other editions of the game, such as the ring of flying or ring of levitation, do not exist in AD&D. They do, however, exist as possible powers of the ring of contrariness, so that might be a clue that one is dealing with a cursed ring and not a bona fide magic ring. One other ring allows flight - the ring of elemental air command. One ring has some bizarre functions that don't replicate spell powers - the ring of shooting stars. Outdoors at night, this ring is able to generate dancing lights, light, ball lightning, and shooting stars. Those last two functions are specific to this ring only. Indoors or underground at night, the ring can produce faerie fire or a spark shower. This last power has no spell equivalent, and is unique to this ring. I would assume that such a ring could be created by a cleric of Celestian the Far Wanderer, or perhaps an elven cleric of Corellon Larethian. The powers seem to be a combination of clerical, druidic, and magic-user spells. Some rings have unique sub-powers or effects that are tied to their operation, or variations of powers based on how they were made. For instance, the ring of regeneration has two varieties: the regular regeneration ring, and the vampiric regeneration ring. One enhances the healing powers of the wearer to regenerate like a troll, the other allows one to heal from attacking other creatures, absorbing half the hit points of damage caused as healing to the wearer's body.
There is no doubt that a magic ring is not a low-level magic item. Surely, there are some varieties that could be presented to low-level parties - these include a +1 ring of protection, ring of feather falling, ring of fire resistance, ring of invisibility, ring of warmth, or ring of water walking. These items are not too overwhelmingly powerful but are very useful to survival at low levels. They also don't provide a terribly large XP value to those who keep them (but could mean a windfall if such were sold for the GP sale value). Most magic rings, however, are very powerful and useful magic items of a permanent nature, so a DM has to be careful when inserting one into their campaign. Also note that since up to two rings can be worn per individual, giving out multiple rings may backfire and make one character more powerful than they deserve. Luckily, the magic powers of rings do not stack with themselves, so no one can run around with two rings of protection +6 and get a -2 AC while basically naked. Effects also may not work in certain conditions - for instance, a ring of protection does not provide an AC bonus when worn with magic armor (although the saving throw bonus still works), however a ring of protection will work with other items of protection, such as cloaks of protection and bracers of defense. (NOTE: This is a big difference between original or Basic D&D and AD&D).
Rings, therefore, are some of the most powerful of the magic items in the game, playing second fiddle only to the most potent miscellaneous magic items or artifacts and relics. They are relatively easy to use for any class or race (including some monsters), but are a pain the ass to identify properly until many experiments and trials are done, sages are consulted, and divination spells are cast. Almost all are permanent items that one can use indefinitely (although some are charged and others have limits to use or penalties if one abuses the power). The only time a ring will not work perfectly is if it is worn by a dwarf, gnome, or halfling, or if it enters a zone of anti-magic. Although a dispel magic spell can destroy some rings, most rings are simply temporarily deactivated when in the area of such a spell, and since such magic must affect a 12th-level caster, this may not always affect them. Rings are some of the most useful and reliable magic items, with hardly any "gotchas" worked into them (something that Gary Gygax is well known for). Those that do have drawbacks are simply in place to keep abuse of the magic ring to a minimum.

