Like Magic items, Rares have randomly selected magical attributes, but if Magic items generally have only one or two, Rare items have much more: up to 6 in both games.
The name of each Rare item is randomly generated, and has no relation to the affixes it bears. It is always composed of two parts, both of which are determined by the item's type.
Rares can have 2 to 6 affixes to them. Some Rare items can also be found Socketed upon Identifying them if they receive the Mechanic's prefix. Affixes are selected by the game for Rare items in the same manner as Magic items. However, it randomly picks each one, with a 50/50 chance of it being a prefix or a suffix. One Rare item can't have more than 3 prefixes or 3 suffixes. (Jewels can only have two of each, instead of three). A single prefix or suffix can't be picked more than once. A Rare item cannot have more than one prefix or suffix from the same group (a set of prefixes or suffixes that have the same effect, in progressively larger amounts). This means you can't get two prefixes or two suffixes that do the same thing on one item. However, a prefix and a suffix with the same effect are possible. Each rare item may only have a single Socket.
In Diablo II Classic, rare items were potentially some of the best items in the game. They are often overshadowed in the expansion due to the variety of powerful rune words and uniques, but particularly good rares can often compete with the best uniques.
Diablo IIIRares can have four to six magical properties, with the exception of guaranteed off-hand item damage bonus (which is a part of the item's own properties, not affixes). Originally, they required identification, like in Diablo II, but as of the pre-expansion patch, they are already identified when they drop. They can have a differing number of sockets depending on the slot type. Although these items are rare, as the name implies, at low character levels, they become more common as the player progresses. Rares are actually the most common item found when at the highest character level.
Their stat rolls are higher than those of Magic Items, but lower than amounts rolled on legendary items.