I’ve been waiting multiple maps to do one of these because it seemed pretty fun, but each map someone got to it first.
Note: This guide is going to be organized based on the colour of the rare sets in game. I am of course doing each set in order: Helmet - Boots, and will label each rare as mining / combat / looting / farming / fishing / misc .I am not going to include the wands as each wand has 4 abilities and there are currently 4 in the game. Here we go!
Harry Potter
Harry Potter Scar - Combat Ultra
Ability: You gain a passive defensive buff via knowledge of when someone is tracking you or is nearby.
HARRY POTTER ROBE - Mining Legendary
Ability: You gain 1.5x the ores from passively mining and 2x while
sneaking.
Harry Potter Trousers - Combat Ultra
Ability: You take minimal knockback from combat.
Harry Potter Boots - Looting Ultra
Ability: You have the ability to auto sell ores outside and get 1.10x the normal price.
Ron Weasley
Ron Weasley Face - Combat Ultra
Ability: After eating a regular golden apple you gain Strength 3, Speed 3, and Nausea 3.
Ron Weasley Hands - Combat Ultra
Ability: Attack multiple monsters at once.
Ron Weasley Pockets - Misc Ultra
Ability: Summon a storage GUI to house any item besides resources or any rares Ultra+.
RON WEASLEY TOES - Undetermined Legendary
Ability: Mine in a 3x3 area for 25 seconds; cooldown is 20 minutes.
Hagrid
Hagrid Beard - Mining Ultra
Ability: Right click ores in the mine to turn them to stone. Using the Bomarda pickaxe with this rare will allow you to mine a lot faster as stone, coal, and iron ore/blocks break faster. Shift in the mine to spawn emerald blocks around you.
Hagrid Guts - Combat Ultra
Ability: Drinking potions while equipped doubles the duration of the effect. Does not work for food like god apples.
Hagrid Shorts - Farming Ultra
Ability: Harvest more Unrefined Pills from breaking melons.
HAGRID BOOTS - Farming Legendary
Ability: 2x passive crop drops. Very slim chance for an “Abundant Harvest” which gives 500x the crops for only one crop. You better be harvesting crack when this happens.
Snape
SNAPE EYES - Combat Legendary
Ability: Ride a player like a damn horse! This only works outside or in gold rushes. You have most control over the player being ridden, however, they can break out of your “grasp”! Apparently, this rare can be pretty buggy in some conditions.
Snape Cloak - Misc Ultra
Ability: Protection against fire damage, fall damage, and traps (when looting outside).
Snape Pants - Combat Ultra
Ability: Upgraded potency of potion effects. For example, Instant Damage II would be Instant Damage III.
Snape Boots - Mining Ultra
Ability: You become magnet man and pull only resources towards you at a considerable speed.
Dobby
Dobby Ears - Misc Ultra
Ability: Wearing grants you the ability to know what other people find outside. It will tell you what ultra, legendary, or mythical the person finds.
Dobby Fingers - Mining Ultra
Ability: When mining Iron or Gold blocks it has a chance to give more. Great for Iron or Gold Rushes.
Dobby Legs - Mining Rare
Ability: Grants the user a guaranteed +1 extra block drop.
Dobby Feet - Misc Ultra
Ability: During a golden grass, punching grass gives you a lot more resources than normal. This is a great ultra to just have ready in your inventory to put on!
Dumbledore
Dumbledore Spectacles - Mining Ultra
Ability: Nearby ores are upgraded to their next tier while mining.
Dumbledore Chestplate - Farming Rare
Ability: Auto harvests crops.
DUMBLEDORE TROUSERS - Misc Legendary
Ability: Gives you 1 level every minute. Killing mobs outside gives lots of money and exp.
Dumbledore Boots - Misc Ultra
Ability: No Fall Damage and 2x experience gain.
Hermione
Hermione Brain - Farming Rare
Ability: Automatically waters nearby crops.
Hermione Sweater - Combat Ultra
Ability: See other people’s potion effects and health.
Hermione Skirt - Combat/Mining Ultra
Ability: Speed 2 whiles holding a sword, Haste 2 while holding a tool.
Hermione Shoes - Combat Ultra
Ability: While shifting you can see who’s near you and how far away.
Newt
Newt Eyes - Looting Ultra
Ability: Killing mobs outside has a chance to give you rare items.
Newt Body - Looting Ultra
Ability: Looting outside chests has a chance to give you gold blocks.
Newt Pockets - Misc Rare
Ability: Shifting lets loose a horde of rats. Great paired with Newt Eyes!
Newt Boots - Misc Ultra
Ability: Hitting your jump key twice will boost you forward a fair distance.
15 second cooldown if used in pvp.*
Draco
DRACO HAIR - Misc Legendary
Ability: Steal 33% of everything sold near you.
Draco Fingers - Combat Ultra
Ability: Right clicking a player picks them up and clicking again throws them in the direction you are facing. They can hit shift and get off your head.
Draco Legs - Misc Ultra
Ability: Every second you shift is another level of speed for 10 seconds. For example: If you shift for 3 seconds, you gain Speed 3 for 10 seconds. The speed is capped at Speed 5.
Draco Feet - Combat Ultra
Ability: Blocking your sword lets you levitate in the air and unblocking your sword will drop you to the ground. Anyone under you will take damage.
Voldemort
VOLDEMORT SKULL - Combat Mythical
Ability: A literal skull that gives you Speed 5 passively and Speed 25 when you shift. Disables the ability to eat God Apples for all nearby players in a certain radius.
INVISIBILITY CLOAK - Misc Mythical
Ability: While you are outside you are permanently jammed and passively gain Invisibility 2. If you are sneaking, you will turn full invis, and your invisibility particles are hidden. Shifting against a wall equal or less than 3 blocks wide thick allows you to phase through said wall.
VOLDEMORT LEGS - Mining Legendary
Ability: Shift to Gain Haste 30 and Blindness for 15 seconds. Passive Haste 4.
VOLDEMORT BOOTS - Looting Legendary
Ability: Autosells found gems outside for 2.50x the normal value.
Miscellaneous
Moody’s Staff - Combat Ultra
Ability: Deal more damage the closer you are to the enemy. Take less damage while blocking.
Golden Snitch - Combat/Mining Ultra
Ability: Right clicking outside provides evasive buffs such as Speed 4 and Jump 4 for 4 seconds, and inside it buffs your mining experience by giving around 3 gold ingots per block mined. This does not negate your normal block drops. Duration is 10 seconds.
Philosopher’s Pickaxe - Mining Ultra
Ability: Efficiency 6, Fortune 2, and upgrades all ores to the next tier on break. Every ore gives 5x the experience, and right clicking turns all blocks of the same type in a vein into gold blocks in a 3x3x3. Great coupled with the Dementor Pickaxe.
Dementor Pickaxe - Mining Ultra
Ability: Changes from Efficiency 1, Fortune 1 to Efficiency 6 Fortune 4 after mining some blocks. Mining a vein of stone turns it into coal, which if you wield both the Philosopher’s Pickaxe and the Dementer Pickaxe, you can right click with the Philosopher’s Pickaxe and turn the entire vein of coal into gold blocks, and mine the gold blocks with the Dementor Pickaxe which has Fortune 4.
Gringott’s Pickaxe - Mining Ultra
Ability: It loses durability as you mine and when its durability is low you can activate an ability that spawns high tier ores in two layers of the mine.
Hufflepuff’s Cup - Combat Ultra
Ability: Right click to make nearby players jump two blocks into the air on contact with ground for 9 seconds.
Hagrid Crossbow - Combat Ultra
Ability: Charge the bow until you hear an alarm-like sound; that’s when you know it’s ready to shoot. Power 10, Punch 3. It does anywhere from 3-7 hearts of damage and a definite bleed effect.
Hagrid Axe - Combat/Mining Ultra
Ability: Sharpness 10, Efficiency 6, Fortune 2. Right click in a mine to create an 11x11x1 hole.
HAGRID HOOK - Fishing/Combat Legendary
Ability: Lure 4, Knockback 2, Fire Aspect 1. Passive 2x chance for fishing up Fishing Specials or Ultra Rares. Hook someone and pull to your position with a 15 second cooldown.
BOMBARDA PICKAXE - Mining Legendary
Ability: Mining has an explosive affect. The explosions can be 3x3x3, 5x5x5, 9x9x9, or a low chance for a large 13x13x13!
LESTRANGE PICKAXE - Mining Legendary
Ability: Efficiency 100 and mining produces obsidian in a random spot near the mined block which gives emerald blocks on break.
MARAUDER’S TRACKER - Misc Legendary
Ability: Pinpoint one’s location by holding the tracker and typing their name in chat. It also shows their coordinates. Right and left clicking works as a normal tracker.
SIRIUS BLACK PICK - Mining Legendary
Ability: Mining coal gives you Haste; mining iron spawns a vein of gold blocks; mining gold mines the vein; mining diamond creates an explosion; mining emerald creates a bigger explosion.
SWORD OF GRYFFINDOR - PvP Legendary
Ability: Hit an estimated 0.5 blocks farther when wielding this sword. 18.5 attack damage. Chance to inflict a Bleed effect dealing pure damage.
RAVENCLAW’S DIADEM - Mining Legendary
Ability: Shift in a mine to enchant every ore in a radius. It lasts for 10 seconds.
RESURRECTION STONE - Combat Mythical
Ability: Only works outside! Come back to life twice. When you have this item in your hotbar, you will be resurrected but you will be stuck at 5 hearts rather than 10, and you cannot regen. You will be given 5 seconds of invincibility after death. On your second life, if you die again you will be put at 2 hearts with no regen but again you gain invincibility for 5 seconds and this time the stone has a chance to drop on the ground for anyone to pick it up. All of this resets once the player enters the prison with or without the mythical.
These are all of the Ultra, Legendary, or Mythical Rares in the game. Please let me know if I forgot anything so I can add it to the list.
Thanks!
EDIT: Thanks for the pin 
EDIT: Finally updated the list! Added farming rares and other sets and updated their abilities after nerfs or buffs.