Many racial abilities, class features, spells, and magic items offer bonuses on attack rolls, damage rolls, saving throws, Armor Class, ability scores, or skill checks.
Bonuses of different types always stack. Bonuses that have identical types don’t stack, except for dodge bonuses and some circumstance bonuses. Untyped bonuses stack unless the bonuses come from the same effect. Penalties aren’t usually typed, but identical types of penalties don’t stack. In this latter case, the worst penalty applies.
Bonuses are classified by type, as described here.
An alchemical bonus represents the benefit from a chemical, usually one ingested prior to receiving the bonus.
This is the bonus that nonmagical armor gives a creature. An effect that gives an armor bonus typically creates an invisible, tangible field of force.
This is a bonus or penalty based on situational factors, which might apply either to a check or the DC for that check. Circumstance modifiers stack with each other, unless they arise from essentially the same circumstance.
When a creature has a competence bonus, it actually becomes better at what it’s doing.
A deflection bonus increases a creature’s AC by making attacks veer off.
A dodge bonus enhances a creature’s ability to get out of the way quickly. Dodge bonuses stack with other dodge bonuses, but they don’t apply whenever a creature is denied its Dexterity bonus to AC.
An enhancement bonus represents an increase in an armor bonus, a natural armor bonus, or a shield bonus. It can also represent an increase in a weapon’s effectiveness or a general bonus to an ability score.
An inherent bonus is a bonus to an ability score that results from powerful magic. A creature is limited to a total inherent bonus of +5 to any ability score.
An insight bonus makes a creature better at what it’s doing by giving an almost precognitive knowledge of factors pertinent to the activity.
A luck bonus represents good fortune.
A morale bonus represents determination. Such bonuses come from mind-affecting effects.
A natural armor bonus is the type of bonus that many creatures have because of their tough or scaly hides.
A profane bonus represents the power of evil.
Creatures gain racial bonuses—usually to skill checks— based on the kind of creature they are.
A resistance bonus is a general bonus against magic or harm. Resistance bonuses almost always affect saving throws.
A sacred bonus relates to the power of good.
Much like an armor bonus, a shield bonus to AC represents the protection a nonmagical shield affords. An effect that gives a shield bonus usually represents an invisible, tangible shield of force that moves to protect a creature.
When a creature changes size due to a magical effect, some of the changes can be size bonuses or size penalties. Such modifiers stack with those granted by natural size or changes in natural size, such as when a monster advances.