Pirates

Pirates are special groups of enemies that can appear in the Item World. These roving bands of enemies appear on random floors to attack the player. They are often strong and difficult to defeat, as their levels are higher than normal enemies. To encounter pirates, you need to spend at least one turn on any floor in the Item World. There is a chance that Pirates will show up on turns 2, 3 or even later, but a Turn 1 absence normally means that the Pirates will not appear.

Disgaea 2
The leader of each pirate crew is carrying one of the Treasure Maps necessary to unlock the Land of Carnage, which is obtained upon defeating them. Having Treasure Maps equipped increases the chance of pirates appearing.

Disgaea 3
Each pirate crew is carrying one of the Illegal Tickets that unlock a stage in the X-Dimension. You can increase the odds of running into pirates by assigning characters to the PPP Club and Tora no Ana Club. Both clubs are unlocked once you defeat your first set of pirates.

It should be noted that there is a glitch in Disgaea 3: Absence of Justice which causes the game to freeze when Masked Pirates are attacked or remain on the Player's pirate ship when the ship tries to depart after the final turn (while Reverse Pirating), and therefore, cannot be defeated. However, these pirates do not carry an Illegal Ticket or have a corresponding trophy achievement, so it's safe to not try seeking them out.

List of Pirates
Below is the list of Pirates, the floors where you can encounter them and the ship they come with.

Disgaea 4
Pirates appear not only after a specific depth but some only appear in specific routes. Pirate crews drop a ship part upon defeat.