No. You get +4 AC, as an armor bonus, meaning it doesn't stack with the bonuses from additional castings of mage armor, actually wearing armor, or wearing bracers of armor.
It does however stack with shield bonuses (such as from the Shield spell), and natural armor (from amulets of natural armor, or bark skin).
No, it gives you a +4 armor bonus to AC. Armor bonuses do not stack with other armor bonuses.
Bonus: Bonuses are numerical values that are added to
checks and statistical scores. Most bonuses have a type,
and as a general rule, bonuses of the same type are not
cumulative (do not “stack”)—only the greater bonus
granted applies.
Ma ge Armor
School conjuration (creation) [force]; Level sorcerer/wizard 1
Casting Time 1 standard action
Components V, S, F (a piece of cured leather)
Range touch
Target creature touched
Duration 1 hour/level (D)
Saving Throw Will negates (harmless); Spell Resistance no
An invisible but tangible field of force surrounds the subject of a
mage armor spell, providing a +4 armor bonus to AC.
Unlike mundane armor, mage armor entails no armor check
penalty, arcane spell failure chance, or speed reduction. Since mage
armor is made of force, incorporeal creatures can’t bypass it the way
they do normal armor.
The only bonuses that stack with themselves are Dodge bonuses, Racial bonuses, and unnamed bonuses (those that just say "bonus"). Everything else overlaps unless they have different bonus types (a +4 shield bonus and a +4 armor bonus would stack to make +8 AC, but two armor bonuses would not, for example).
Multiple Natural Armour bonuses also stack with each other.
They absolutely do NOT. Many items and effects give an ENHANCEMENT bonus to natural armor, which stacks with NATURAL ARMOR bonuses.
At no point do natural armor bonuses stack with other natural armor bonuses.
Hmmm - can't find any reference to them stacking now. Could have sworn they did. My bad.
With Natural Armor, sometimes an ability doesn't give natural armor normally, but instead gives you an increase in natural armor.
That stacks with other NA, because that is literally what it says to do.
The NA from the Dragon Disciple, for example:
Natural Armor Increase (Ex)
As his skin thickens, a dragon disciple takes on more and more of his progenitor's physical aspect. At 1st, 4th, and 7th level, a dragon disciple gains an increase to the character's existing natural armor (if any), as indicated on Table: Dragon Disciple. These armor bonuses stack.