Two armor bonuses does not stack, everything else will
Bonuses with the same name or from the same source do not stack, as explained on the glossary:
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.
The important aspect of bonus types is that two bonuses of the same type don’t generally stack. With the exception of dodge bonuses, most circumstance bonuses, and racial bonuses, only the better bonus of a given type works. Bonuses without a type always stack, unless they are from the same source.
That means two armor bonuses will not stack, only the highest will be applied, two natural armor bonuses will not stack, two deflection bonuses will not stack, and so on.
If you look at this image from the SRD, you will see that the Snakeskin Tunic uses the Chest magic item slot, while the Mithral Shirt uses the Armor magic item slot.
Each slot can only gain the benefits of a single magic item, but your character will benefit from all magic items from all those slots at once, assuming the other rules are respected (like stacking bonuses).
When a character wears a slotted wondrous item he cannot gain the benefit from a wondrous items of the same slot until the first item is removed. Of course, a character may carry or possess any number of slotted items of the same type, but additional items have no effect until they are worn.
In other words, your character will gain the benefit of both magic items (except for the armor bonus).