There are 8 crafting tradeskills that are used to create items that can either be worn or used to enhance your character in some other way. Nearly all of these directly benefit from a specific gathering tradeskill, but not all. You may have two crafting professions learned at any given time should you so choose.
Alchemy
The Alchemy tradeskill is used to create potions, elixirs, and flasks, as well as to transmute certain high level items into other items. Herbs are the most common ingredient in Alchemy recipes, so Alchemy benefits most from being coupled with the Herbalism gathering skill.
Inscription
The Inscription tradeskill was recently added in the Wrath of the Lich King expansion. Scribes can create glyphs that a person can "inscribe" or attach to their spellbook in order to enhance specific spells or abilities. They can also create Inscriptions that enchant shoulder slot items, create magical cards, and create off-hand frills that benefit spellcasters. Scribes create ink out of herbs to use in their Inscriptions, so the Inscription profession benefits most from being coupled with Herbalism.
Leatherworking
The Leatherworking tradeskill allows a player to create leather and mail armor as well as drums that grant temporary buffs to the leatherworker's group. They can also craft armor kits that any player can apply to certain armor slots to grant bonuses. Leatherworking logically uses a lot of leather, and therefore benefits most from being coupled with the Skinning gathering skill.
Blacksmithing
The Blacksmithing tradeskill is used to craft mail and plate armor, as well as weapons. Metal bars are the primary material used in Blacksmithing, so it logically benefits most from the mining gathering skill.
Engineering
Engineers are masters of technology, gadgets, and explosives. The engineering tradeskill is used to create fun items, trinkets, pets, mounts, head gear, and more! There are a lot of neat tricks that an engineer can learn and an endless amount of gadgets are at their disposal. Most things an engineer creates are made out of metal, so mining is the gathering skill most commonly associated with it.
Jewelcrafting
Jewelcrafting was the new profession introduced in The Burning Crusade expansion pack. Jewelcrafters can craft rings, necklaces, and trinkets, as well as a few fun limited use items. They can also cut gems, imbuing them with special powers depending on their color and cut. These gems are used to enhance gear items that contain sockets. Gems are found while mining and when the jewelcrafter prospects ore, so the most logical gathering pairing is the Mining tradeskill.
Tailoring
The tailoring tradeskill is different in that the materials needed for it are not found with a gathering tradeskill. Varying types of cloth drops of mobs in the open world, no matter who picks them up. Tailors can use this cloth to craft cloth armor, cloaks, bags, and magical spellthreads that are embroidered onto armor to give it bonuses. Because tailoring produces a lot of magical items and doesn't require a gathering skill, it is often combined with Enchanting.
Enchanting
Enchanting, much like tailoring, isn't associated with a gathering skill. Rather, the materials needed for enchanting are gathered by using the Disenchant skill associated with the trade. Magical items, ie: Uncommon, Rare, or Epic quality items with bonuses, can be disenchanted into materials, destroying the item. Those materials can then be used to add bonuses to other armor or weapons. Because Enchanting uses a lot of magical items and doesn't require a gathering skill, it is often combined with Tailoring.