I have always seen clerics wearing armor, and I have never seen them suffer from arcane spell failure. Yet when I check the rules I cant seem to find anything which allows them to not suffer these penalties. Have I somehow overlooked this or does the class granting armor proficiency grant it the ability to wear that armor and not suffer from ASF? It is just the fact that its arcane spell failure and not spell failure?
From the rules for arcane spell failure chance:
Armor interferes with the gestures that a spellcaster must make to cast an arcane spell that has a somatic component. Arcane spellcasters face the possibility of arcane spell failure if they’re wearing armor. Bards can wear light armor and use shields without incurring any arcane spell failure chance for their bard spells.
Arcane spell failure applies only to arcane spells (and then, only to arcane spells with somatic components, and even then bard spells are excepted if the armor is light).
@KRyan has the relevant rules quote.
ASF only applies if the Cleric tries to cast an Arcane spell.
This is not as flippant as it sounds since there a number of ways for a Cleric to gain the ability to cast arcane spells. The most common is by gaining levels in a class that casts Arcane spells.
A Cleric's ability to cast clerical spells while wearing armor does not give it the ability to cast other kinds of spells while wearing armor unless he has some other method of doing so (Bard levels for Bard spells, etc.).