Farming - Skinning, Mining, and Herbalism
Farming professions are good professions to choose if you want to make gold with no risk and enjoy farming. If you choose farming professions you will ALWAYS be able to make money using them. Simply go out and spend some time gathering materials and then sell them on the AH. Some people find this an enjoyable way to spend their time and if you are one of these people you should definitely not give up your farming professions. If, however, you don't like to farm but you have farming professions because they make money or you think they provide you free mats to craft with, you should switch your professions as those "free" mats aren't free as they cost you time. From a gold making perspective there are almost always better ways to spend your time than farming, thus I wouldn't take farming professions as my first choice.
Crafting - Blacksmithing, Engineering, Leatherworking, Tailoring, and Alchemy.
Crafting professions are the worst professions to choose long term if you are interested in gold making and you are limited in how many toons you have. The reason for this is that the crafting professions tend to be a bit hit or miss in terms of profitability. Depending on your server and the patch you may, or may not, be able to make money with crafting professions. While there may be times that people with a certain crafting profession are able to make the most money on your server I still would not choose to take the profession as this will change with time. After a few weeks or months, or when the next patch comes out, or some other event occurs the profession may no longer be profitable and you will be looking to change professions again.
The one exception to this rule is Alchemy. Alchemy generally won't make you rich by itself but it can be used in conjunction with Jewelcrafting to offer additional profitability to the shuffle. In addition the transmutes available to alchemists can often be used to make a decent profit with very little time invested. If I had to choose one of the crafting professions to take I would definitely make that profession alchemy without a second thought.
Converting - Inscription, Jewelcrafting, and Enchanting.
These professions are usually lumped in with crafting professions (even Blizzard makes this mistake). These professions are different from crafting professions though because they convert the materials gathered by people with farming professions into new materials! They can then use these new materials to make other items. Converting professions are the best professions to have (unless you just like to farm) in terms of gold making. This is because these professions have two separate ways to make money! You can either convert farmed mats into the basic mats for your profession and sell those OR you can craft items to sell on the AH. If you are an enchanter you can make and sell enchanting mats OR enchants, if you are an inscriptionist you can make and sell inks OR glyphs and cards, if you are a jewelcrafter you can make and sell raw gems OR cut gems. This leads to long term profits because usually if the market in one side of your profession dies down the market for the other side of your profession will grow! If the market for your goods gets too crowded or dies down chances are that you can just switch your production focus and continue to make lots of gold without changing your profession at all. Thus if you want to choose professions that you won't have to change, will make money for you day after day, and don't require hours farming for materials then you should definitely choose to train in two of the converting professions.
The Power Word: Gold Guide Free is Copyright © 2011 Jim Younkin. Guide contributors include Bangkok Bill and fluxdada.