Stat Caps are a statistical boundary on the the maximum values of a unit's stats.
Overview
Stat caps are hard limits on the maximum value a unit's individual stats can reach. If a stat reaches its cap, it cannot rise any further unless the unit promotes to a higher class tier and is granted a higher stat cap. Stat boosters cannot be used to exceed a unit's current caps. However, special stat bonuses may exist, such as the +5 Defense that Ike receives from equipping Ragnell, that will apply despite the unit having reached their natural cap.
Stat Caps per Game
Fire Emblem: Mystery of the Emblem
The HP cap is 52 and the cap for all regular stats is 20.
Fire Emblem: Genealogy of the Holy War
The HP cap is 80. The cap for all regular stats is equal to the base stat+15, and is usually in the range of 15-30.
Fire Emblem: Thracia 776
The HP cap is 80 and the cap for all regular stats is 20.
Fire Emblem: The Binding Blade, Fire Emblem: The Blazing Blade, Fire Emblem: The Sacred Stones
In the GBA Games, the stat caps for unpromoted characters are 60 in HP, 30 in Luck, and 20 in Strength, Magic, Skill, Speed, Defense, and Resistance. Upon promotion, the stat caps increase for all stats (excluding HP and Luck) depending on the character's class and gender.
Fire Emblem: Path of Radiance
The stat caps are similar to those in the GBA games, except the HP cap for unpromoted characters is 40 and rises to 60 upon promotion. The Luck cap has also been raised to 40 for all classes. Special classes like the Laguz can have an HP cap up to 80 and regular stat caps up to 40.
Fire Emblem: Shadow Dragon
The stat caps are almost identical to those in the GBA games, with the only differences being the addition of the Magic stat, and the caps not being affected by the character's gender.
Fire Emblem Awakening
The stat caps are almost identical to those in GBA games, except they only occur in base classes (e.g. Cavalier, Knight, Mage, Myrmidon, etc.) with base HP cap of 60 and base Luck (and some other stat) cap of 30. Upon promotion, the base HP cap will be increased to 80, while usually the Luck (and some other stat) cap will be increased to 45. In addition, depending on the character, there are stat modifiers that will determine the characters' max stat caps, whether they are increased or decreased.
Fire Emblem Fates
The HP cap goes to 70 being the highest General and Berserker you could increase this by using skills. All other stats are maxed between 20-40. They can be increased and decreased for about a turn, like Awakening. And like in Awakening, each character has their own stat modifiers (see Awakening).