Regen (short for Regeneration and also known as HP Regen and FP Regen) is a special status effect that appears in the Paper Mario series.
In Paper Mario: The Thousand-Year Door
In this game, there are two types of Regen that appear. As stated above, it being HP Regen and FP Regen.
HP Regen
HP Regen is mainly associated with HP being restored over time. There are numerous of ways to obtain the HP Regen status. The best way is to use a Slow Shroom that gradually restores 2 HP for the course of 10 turns. Certain dishes can also gradually restore HP over time but is usually different each time (such as the Meteor Meal restoring 2 HP for 3 turns but also restores 7 HP on the spot and the Couple's Cake restores 2 HP for 10 turns).Badges such as Happy Heart and Happy Heart P also does HP Regen but only restores 1 HP for the entire battle. This functions as the opposite of the Poison effect.
FP Regen
FP Regen works similar to HP Regen but only for FP. The Gradual Syrup is a good item to use to achieve the FP Regen status. It restores 2 FP for the next 10 turns. The Lucky Start badge may grant the FP Regen status as also the Happy Flower badge.
In the Mario & Luigi series
Mario & Luigi: Dream Team
Certain gear effects can give the wielder this condition in Mario & Luigi: Dream Team. Mario and Luigi can equip Angel Bangles to give themselves this status effect in Mario & Luigi: Dream Team, regaining 20 hit points (abbreviated HP) and 10 special points (abbreviated BP; literally "Bros. Points") at the start of their turn; however, the effect is temporarily dispelled from the wearer if something stuns him or sets him on fire. There are also HP Bangles which restore hit points and BP Bangles which restore Special Points.
Mario & Luigi: Brothership
This effect returns in Mario & Luigi: Brothership, where the Sharpcask can hunker to gain a souped-up version of this status effect in conjunction with an exaggerated defense boost, doing so the first time it reaches 75% total health. Luigi can counter this with his Luigi Logic skill, manipulating the conveyor belt so that the Sharpcask gets crushed by falling crates; if Luigi is successful, these status effects get replaced with Dizzy and DEF-Down.