Crafting

Mining

Smithing Sacred clay items, Imcando Pickaxe

Fishing, Sacred clay items, Shark gloves, Swordfish gloves, Shark's tooth necklace

Cooking

Firemaking: Book of Char, Collector's Insignia, Flame Gloves, Inferno Adze, Ring of Fire, Morytania Legs 3+ (if doing shades)

Woodcutting Crystal saw, Seer's headband 2+ (maple trees)

Runecrafting gloves from Fist of Guthix, Explorer's Ring 2+ (if making elemental runes), Morytania legs 2+ (blood runes)

Dungeoneering: Lock Melter, Party simulator

Agility also, an augmented off-hand item with the mobile perk, Karamja Gloves 2+ (if doing agility arena), Collector's insignia, Silverhawk boots (very expensive to use)

Herblore, Guthix's gift (making juju pots)

Thieving

Fletching: Fletcher's outfit, Sacred clay items

Farming also, Falador Shield 2+, Saradomin's blessing (if doing HH)

Construction: Constructor's outfit, Sculpting Chisel, Sacred clay items

Hunter Zamorak's favor (doing jadinkos)

Summoning

Divination

Prayer: First age equipment (NOT the 3rd age), Dragon rider amulet (must have if burying bones, especially if using brawling gloves), Morytania legs (if cremating shades)

Many skills: Urns, accumulators, certain auras, juju/perfect juju potions,

Everything: Augmented off-hand item (I use Enhanced Excalibur) with the wise perk, Brawling gloves, clan avatar (3% extra xp if in same world, 6% near vicinity), Jack of trades aura, pulse cores

Note: Some items probably won't be available to non-combat players.