Rank

Rank is an informal term used in reference to an item and how strong it is.

Description
All items have a rank from 1 to 40(with some exceptions) assigned to it, indicating how strong it is relative to others of its same category. Higher ranked items not only have better stats but also come with stronger Specialists. Inside the games, items of the same category will always appear listed in ascending rank.

Shops will only sell items up to a certain rank, depending on your Customer Rank. Items of rank above that limit must be obtained in the Item World either as a bonus reward, from a treasure chest, or by stealing it.

Rank 40 items, being the strongest in the game, have the special property of always coming at Legendary Rarity. However, they also have the limitation that they can only be obtained by stealing from an Item God or Item God 2(details here).

Below is a list of specifics for each game.

Disgaea: Hour of Darkness

 * Shops can sells items up to rank 38.
 * This game has a few items above rank 40:
 * Nemesis: Rank 41 Monster Weapon. Must be stolen from Tyrant Baal.
 * Nemesis MK-2: Rank 42 Monster Weapon, comes at level 100. Must be stolen from Prinny Baal.
 * Prinny Costume: Rank 41 Armor. Must be stolen from Prinny Baal.

Disgaea 2: Cursed Memories

 * Shops can sell items up to rank 38. However, the special shop that can appear in Mystery Gates can have rank 39 items.
 * Lover Specialists can't spawn on items of rank 5 or lower.

Disgaea 3: Absence of Justice

 * Shops can sell items up to rank 30. Rank 31 to 34 can be obtained in regular Item World, while rank 35 to 40 require entering Item World through Land of Carnage.
 * In Absence of Detention, new rank 41 weapons and armor can be obtained from the Item God 2 of a rank 40 item.

Disgaea 4: A Promise Unforgotten

 * Shops can sell items up to rank 30. Rank 31 to 34 can be obtained in regular Item World, while rank 35 to 40 require entering Item World through Land of Carnage.
 * In A Promise Revisited, new rank 41 weapons and armor can be obtained from the Item God 2 of a rank 40 item.

Disgaea D2: A Brighter Darkness

 * Shops can sell items up to rank 30. Rank 31 to 34 can be obtained in regular Item World, while rank 35 to 40 require entering Item World through Land of Carnage.
 * Rank 39 Items can now be bought in the shop but only if the player defeats Pringer Z in order to unlock Product Rank 12.
 * If entering an item of at least Rank 12, only Rank 35+ items will appear in chests and the Bonus Gauge.

Disgaea 5: Alliance of Vengeance
A complete list of all items with their respective ranks can be found here

Disgaea 6: Defiance of Destiny
A list of the item ranks of D6 provided by u/niquitwink on Reddit: