
Jeraa |

Generally, anyone can use any armour. Non-proficiency just adds the armor check penalty to your attack rolls and "all skill checks that involve moving", instead of just strength/dexterity-based skills.
And if the armor check penalty is -0, like it is for the haramaki and silken armor or a mithral buckler, there is no drawback when worn if non-proficient.

Wheldrake |

Arcane spellcasters like wizards aren't really supposed to be wearing any armor at all. That's why they have the mage armor spell and why bracers of armor exist.
But as others pointed out above, armor that has a very low spell failure chance can be worn with little trouble.
To an old grognard like me, though, it still feels like cheese. <g>

Claxon |

Anyone can use any armor, but you might take penalties for doing so.
If you meant "what armor can a 9th level progression arcane caster use without penalties" the answer is haramaki or silken ceremonial armor.
If you happen to be a psychic caster archetype then you can go with mithral kikko armor which has an ACP of 0 and psychic spells don't incur spell failure chance.

Cantriped |

The Harimaki and Silken Ceremonial Armor (from Ultimate Combat and/or Ultimate Equipment) are both inexpensive mundane armor with an armor check penalty of -0 and arcane spell failure chance of 0%. Certain feats combinations will eventually allow primary arcane casters to cast in heavier armor, and there are a few arcane spellcasters who can cast in armor natively (bards, bloodragers, and Magi for example). Magi in particular can eventually cast in heavy armor without penalty, but you rarely see it done because they either trade that feature away in an archetype, or remain in "lighter" armor because of their tendency to be Dex-Based.