With the addition of Ability Power in Update 11, a new weapon designed around it would be really cool

Something like a staff that deals damage based on a percentage of your Ability Power instead of its own base damage. Thematically, I want to be a powerful mage blasting enemies with spells, but it seems odd for a mage pull out a sword or an axe as my weapon, right? Why not a wizard's staff, then? A Vault Staff!

The Vault Staff would be a "ranged" weapon (not truly ranged with a projectile or anything, just a melee weapon with a longer reach than the sword or axe) that uses Ability Power as its damage source and unique "magical" abilities. It would have a bit slower attack speed than the axe, but be able to have much higher attack range - nothing insane, maybe +3 range as the high roll at the VERY highest level. To keep that range balanced, it would also have no knockback at all, so kiting mobs wouldn't be completely trivial.

My initial idea was for the staff to give Ability Power as an implicit and have every staff convert the same percent of AP into damage for basic attacks, but the thought process behind putting AP on armor instead of weapons seems to be for players to not feel required to hold a weapon at all times and be able to throw out powerful spells while breaking chests or mining, etc. So instead, the implicit should be what percent of AP is converted into damage. Low level staffs might roll up to 20% for max rolls (depending on how much AP is expected/possible from armor - staffs should be able to reach much higher damage per attack than swords/axes, but would require good rolls on 4 armor pieces and the staff itself in order to do so), while high level staffs might go up to 50% or more.

So that's pretty cool - you're using AP to deal damage even with your basic attacks, not just abilities. But to make it really feel like a wizard's staff, let's give it some unique suffixes! Swords and axes can roll the various clouds and effects like stunning, shocking, lucky hit, and sweeping hit (for swords). For Vault Staffs, remove all of those and give them their own unique "elemental" effects - they get a percent chance to inflict a particular status on your target with each attack.

For instance, "Pyro Chance" would set the target on fire, dealing damage over time and increasing the damage taken while on fire. "Poison Chance" would poison them for damage over time and reduce their damage output. "Ice Chance" would slow their movement and attack speed. "Gale Chance" might be a strong knockback effect. "Growth Chance" covers the target in vines/flowers and attacking them restores a small amount of health and mana. Maybe some effect for water and earth that I'm not creative enough to think of. And, moving away from the "elemental" theme, a "Charm Chance" that lets you Taunt: Charm a single target or a "Necromancy Chance" that resurrects the mob to fight for you if you kill it within a few seconds would also be exciting effects.

I would absolutely love to see something like this added to the game to diversify weapons a bit and let me play as a full-on mage instead of always being a swordsman who can cast a few spells while beating mobs with my sharp metal stick.