As with other sources of AC, natural armor bonuses granted by persistent feats (as compared to those with spell-like abilities) are considered base bonuses and therefore stack with each other as well as the highest source of one other enhancement bonus (such as the Barkskin spell). This has the effect of increasing natural armor's overall bonus to Armor Class. A Red Dragon Disciple's natural AC bonus is an example of a class feat which grants a persistent natural armor bonus that stacks with others, such as a Yuan-ti pureblood's scaled skin feat.
Otherwise, natural armor bonuses stack with all other bonuses to AC except other natural armor bonuses.
A natural armor bonus doesn't apply against touch attacks.