Whether or not things stack are listed explicitly within the spell or enchantment bonus. Spells and short-term buffs stack together.
For example, a raging barbarian is buffed by his bard's Inspire Courage, and gets a wizard to give him Mage Armor; he receives all bonuses, buffs and/or debuffs associated with these abilities.
Feats and weapon enhancements do or do not, depending on your GM.
EDIT: I am not correct, do not listen to me
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This is partly covered on pages 208 and 209, which deal with magical bonuses.
"More generally, two bonuses of the same type don't stack even if they come from different spells or from effects other than spells."
The exception to this rule are dodge bonuses, most circumstance bonuses, and racial bonuses.
"Different bonus types: The bonuses or penalties from two different spells stack if the modifiers are of different types. A bonus that doesn't have a type (known as untyped) stacks with any bonus.
Also on page 208, Bonus Types:
"With the exception of dodge bonuses, most circumstance bonuses , and racial bonuses, only the better bonus of a given type works. The same principle applies to penalties--a character taking two or more penalties of the same type applies only the worst one, although most penalties have no type and thus always stack."
So, basically, if the bonus has a type, then it doesn't stack with other bonuses of the same type, with the exceptions listed above. Not all bonuses have types.
Some bonus types *off the top of my head* would be:
Enhancement
Circumstance
Dodge
Size
Divine
Competence
Resistance
Armor
Shield
Morale
and so on.
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Generally bonuses of the same type do not stack.
From the PRD
And also:
Combining Magic Effects
Spells or magical effects usually work as described, no matter how many other spells or magical effects happen to be operating in the same area or on the same recipient. Except in special cases, a spell does not affect the way another spell operates. Whenever a spell has a specific effect on other spells, the spell description explains that effect. Several other general rules apply when spells or magical effects operate in the same place:
Stacking Effects: Spells that provide bonuses or penalties on attack rolls, damage rolls, saving throws, and other attributes usually do not stack with themselves. More generally, two bonuses of the same type don't stack even if they come from different spells (or from effects other than spells; see Bonus Types, above).
Different Bonus Types: The bonuses or penalties from two different spells stack if the modifiers are of different types. A bonus that doesn't have a type stacks with any bonus.
Same Effect More than Once in Different Strengths: In cases when two or more identical spells are operating in the same area or on the same target, but at different strengths, only the one with the highest strength applies.
Same Effect with Differing Results: The same spell can sometimes produce varying effects if applied to the same recipient more than once. Usually the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.
One Effect Makes Another Irrelevant: Sometimes, one spell can render a later spell irrelevant. Both spells are still active, but one has rendered the other useless in some fashion.
Multiple Mental Control Effects: Sometimes magical effects that establish mental control render each other irrelevant, such as spells that remove the subject's ability to act. Mental controls that don't remove the recipient's ability to act usually do not interfere with each other. If a creature is under the mental control of two or more creatures, it tends to obey each to the best of its ability, and to the extent of the control each effect allows. If the controlled creature receives conflicting orders simultaneously, the competing controllers must make opposed Charisma checks to determine which one the creature obeys.
Spells with Opposite Effects: Spells with opposite effects apply normally, with all bonuses, penalties, or changes accruing in the order that they apply. Some spells negate or counter each other. This is a special effect that is noted in a spell's description.
Instantaneous Effects: Two or more spells with instantaneous durations work cumulatively when they affect the same target.
Most all bonuses have a type, but not all. Any bonus with out a type stacks with everything but itself.
Kilbourne, in your example, lets say that both are level 1. The barbarian gets the following:
From Rage:
+4 moral bonus to STR
+4 Moral bonus to CON
+2 Moral bonus to Will Save
-2 to AC (reckless)
From Inspire Courage:
+1 competence bonus to attack
+1 competence bonus to damage
(the +1 moral bonus to charm and fear are already handled by the +2 will save from rage, unless there is a charm or fear spell that offers a Reflex or fort save out there that I do not know of.)
From the Mage Armor:
He gets his AC from his armor, or the AC from mage armor, which ever is greater. For example, if the barbarian is wearing studded leather (+3 AC) then mage armor would over-ride that (since both are armor bonuses) and the barbarian would have an AC of +4. If he was wearing chainmail (+6) then he would gain nothing from Mage Armor.
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There are a couple of wacky exceptions to note though... most specifically, how Amulets of Natural Armor don't actually grant Natural Armor, instead they grant an Enhancement bonus to natural armor. They would thus stack with natural armor granted by the various polymorph flavors that can turn you into a monster that has natural armor.
Happier, I have altered my previous post to reflect new information.