Professions

Look in the Auction House for items that sell for good prices, but don't have a big supply in the market, so your prices won't get much competition.
Sometimes you can make money by crafting items with ingredients supplied by other players who give you a tip to make the item. This is not necessarily a reliable source at low levels, but it can be a good supplemental income source at higher levels, particularly if you have good recipes. And if you can charge for the customer using your materials (as opposed to materials supplied by him/her), you can mark those up.


Gathering skills
Mining, Skinning, and Herbalism are all good money-making professions, particularly at higher levels.
With Mining, from the moment you take the skill you can make good money selling stacks of the bars or ores in the Auction House. Blacksmiths, Engineers and Jewelcrafters are interested in the bars, while Jewelcrafters and even other miners may want to buy the ores. Make sure to check the relative prices of ore versus bars before smelting. As your skill increases, so does your earning potential. At the maximum level you may smelt Titansteel for a daily fee.


Skinning is both highly profitable and convenient, in that you will be skinning the monsters that you're already killing as you level. A skinner starts by collecting relatively worthless ruined leather scraps, but soon moves on to light leather, which can be sold for a good profit. An excellent way to farm leather is to skin the kills of other players, especially if you are following along in the wake of a group. However, do wait to start skinning until it's clear that the other player has abandoned the kill. Don't assume that the other player doesn't skin just because they are not a leather-wearer, for example. Note that your chances of getting a better grade of leather increases with your experience; it is possible, though rare, to get light leather from rabbits. Higher grades of leather yield higher profits. A skinner/miner has potent earning power through the auction house, but often runs out of inventory space.


Herbalism is also a good source of money. Herbs are required by alchemists and scribes. Unlike ore which is found only in rocky areas, herbs can be found in many places. Be sure to check on the auction house for what herbs are in demand for a high value; often a lower level one is very valuable, so you can farm an area you already know for quick money.


Consider getting the Gatherer addon. This maps nodes and herbs on your minimap, allowing you to visit these places again and again if you are farming. Gathering professions won't be covered more in depth, as making money from them is fairly straight forward. 


Blacksmithing
Common item recipes to look for include:
Plans: Iron Shield Spike (drop)
Plans: Steel Weapon Chain (drop)
Plans: Iron Counterweight (drop)
These items sell well for decent money, even though they are common quality items. Beware, these recipes can be pricey if you buy them, so try to get a bargain and ask around to see if you are getting a good price.
Blacksmiths should also watch the prices for "Needed by" items such as the metal rods used by enchanters, and compare the price for the raw materials. For example, a Golden Rod requires
1 Gold Bar
4 Coarse Stone
There's a good chance you can buy the raw materials for 25% - 75% of the going rate of the finished item, or mine them for free. The fee for an 8 hour auction is only 1 silver, so you can afford to re-auction rods that don't sell the first time. Be careful of making too many rods or other parts of a kind at once, though, as you may get stuck with them for a long time when others produce the same item and set a cheaper price to it.


Engineering
A good money maker for Engineers are Scopes, which are all crafted by engineers and essential for hunters.
Certain quests require items that can be crafted. A couple of examples:
Alliance only:Bronze Tube (for The Touch of Zanzil (Rogue only), Look To The Stars) and Just a Few More 
Things...
Horde only: Deadly Blunderbuss (for Warsong Saw Blades)


Tailoring
There is usually good money to be made selling bags, particularly the upper-level bags. This is particularly profitable if you are able to farm the majority of the materials.


Alchemy
There is a constant market for transmutations. If you are capable of doing these, you can charge an upcharge on each of those transmutes. A player who logs on his/her character each day, and sticks to it, can generate a significant subsidiary revenue scheme through transmutes. Likewise, if you have a transmute that allows you to transmute a lower value element (such as Earth) into a high-priced one (like Water or Fire), you can make a cool 15-20 profit every day by simply doing your transmutes.
Arcanite Bars still remain a great source of income for Alchemists due to its continuous demand.


Jewelcrafting
Crafting gems is profitable if you have the right designs. Usually only the high level jewelcrafting (JC) are sought for gems, but you can make gold at low levels from JC too!
Jewelcrafters can create jewelery for other players, which can make big profits. Often players buying for their alts will invest in low-level rings and necklaces, simply as rings and necklaces from quests are hard to find. You can make a tidy sum by selling these items in the Auction House.
Jewelcrafting also offers players the Prospecting ability; players can break down most Mining ores to find gems used in Jewelcrafting. The Enchantrix addon can calculate the prospecting value of an ore, and when combined with the Auctioneer addon, you can compare the prospect value to the ore's value and determine whether it has a fair chance of producing a profit. For example, on most servers Tin Ore has a significantly higher prospect value than the ore itself, and players can make a tidy profit by prospecting tin from the AH. The low skill needed to prospect tin ore makes this a great profession choice for bank alts!


Inscription
Glyphs are pretty cheap to produce and some of them are highly sought after, especially those learned at higher levels. Learn which glyphs are in demand and you may get a nice amount of gold by selling them. Don't assume that a high average price of a glyph means that it is in demand; if nobody is buying it, it doesn't matter what the price is.
You should also further develop your inscription skill through minor and Northrend Inscription Research. If you're lucky, you may get a glyph that people want and not every inscriber can make, which can give you more gold. Research them every day to get those high yield recipes faster.
Additionally, you can make tomes held in the off-hand and the Darkmoon cards. These take more materials to make, but the tomes are classified as rare items and can fetch a good price, and even the lower level decks of cards can get you a BoE rare to sell.


Enchanting
While enchanting is generally considered expensive to level, you can make a profit with it as soon as you start disenchanting for profit. It is not unlikely that almost any green item in this case will have a buyout price for a lot less than the materials it disenchants into. Likewise, it is lucrative to check the auction house for green items with unpopular suffixes, such as "of the Gorilla," with low starting bids.
You may want to get a another player or friend to disenchant items for you. Of course offer them some kind of fee or tip for their time, your overall profit will be greater.
Selling enchants can also make some money, but usually only when you have very high level (over 400). Thus, enchanting is isn't really recommended as a good early money making source, particularly because its leveling costs are quite high.
If you use a dedicated banker alt, that does nothing but work the Auction House, have him/her pick up enchanting, so this character can disenchant low-level items.