As others have stated, mining is one of the fastest ways to make money.
As a Holy Paladin:
North part of Netherstorm (Manaforges, 2 demon camps, Socretar's Seat, raptor dome
Blade's Edge Mountain (avoid the flying only plateaus)
Circle around Shadowmoon Valley and Terokkar (ignore Deathforge/Hand of Guldan)
As a DPS Warrior:
Caves in Nagrand
Blade's Edge Mountain (avoid the flying only plateaus)
Find yourself a Jewelcrafter that will buy your adamantite ore for 21-22g a stack or so and one that will also buy Fel Iron for 8-10g a stack and sell it all to him (don't bother auctioning the ore for the most part). To get rid of the Khorium and Eternium you'll have to auction it in very small quantities at a time by putting 2-3 auctions of 1 bar when there isn't a lot on the AH. Also keep your eyes open for people wanting to buy large amounts of Khorium and Eternium for profession skill ups.
Try and sell the Primal Earth for 45-50g a stack and try to keep single Primals and Motes listed at all times. This goes for the other types of primals too: you can sell a single mote for a ridiculous amount of money if you check every type and put them up 1 at a time - we're talking about 4-5g a Mote of Fire and 1g a Mote of Earth on a good day.
Sell the green gems on the AH one at a time (or 3 at a time for transmutes) - but this isn't all that profitable.
Keep or sell the rare gems (you're likely to end up needing them for yourself to be able to find someone that's desperate for a particular kind of gem - beats trying to undercut the Jewelcrafters).
You can also just get a Jewelcrafter to prospect your ore (or do it yourself) and play the AH/trade game. But I find that JCs expect annoyingly high tips for prospecting 2000 adamantite ore and it takes a very long time to prospect large amounts of ore compared to selling all of it.
For Engineering, always keep up the required materials for The Soul Cannon of Reth'hedron - Quests - World of Warcraft
on the AH (2 Felsteel Bars, 1 Adamantite Frame, 1 Khorium Power Core) and put them up at ridiculous prices if nobody else has them listed. When Netherwing mounts came out, I was selling Frames for 20-30g and Power Cores for 60-70g. You can also keep a supply of Khorium Scopes (Khorium Scope - Items - World of Warcraft
) and sell them for 80-100g each when there are none listed on the AH - they're also an excellent item to skill up on if you're patient enough to farm the recipe. I went from 360ish to 375 Engineering crafting those and I sold most of them for 90g+.
Blacksmithing is one of the worst professions to make money unless you can get your hands on the more common crafted recipes that require Nethers (Plans: Bracers of the Green Fortress - Items - World of Warcraft
would be one of the best) - but you still need to run heroics and actually win the Nether to be able to sell it in the first place. You might be able to make some money selling Weight/Sharpening Stones, but a lot of people skill up on those at one point when leveling Blacksmithing, so it's unlikely there won't be any available on the Auction House.
Skinning/Leatherworking is surprisingly good to make money with - if you're a DPS class. Not a lot of people actually skin and even less people actually go out and farm leather. The more exotic skinning drops (Cobra Scales/Nether Dragonscales etc) can sell for ridiculous prices to people who need them - not like there's anybody that farms those on the same scale that primals/ore's farmed up. Clefthoof Leather is another great money maker since you get the Clefthood Leather and the Clefthoof Meat at the same time, plus the normal leather. Leather leg enchants are an amazing way to make money, especially if you get Nethers and sell the epic ones. Always make sure that you have the following in various stack sizes on the AH: Clefthoof Leather, Heavy Knothide Leather and Cobra Scales.
Herbalism's money making potentials are entirely dependent on how fast you can kill the trees in Skettis or on how well you can farm Nightmare Vines. Hunters and Priests can farm Ancient Lichen from instances (SP comes to mind). Sanguine Hibiscus can also sell fairly well if you want to solo farm Underbog - Underbog's for Hunters only however. In any case, selling the Fel Lotus and the Nightmare Seeds is a huge money maker, along with the herbs themselves.
Alchemy's biggest money maker is Elixir spec and flask selling. Make sure to have flasks listed on the AH during prime time or before your server's guilds start raiding. If there's no Flasks of <insert favorite flavor> available except your 40g flask, people will buy yours for that price. You can count on laziness and procrastination to keep selling flasks at ridiculous prices if you take a few minutes every day to list them accordingly. Make sure not to list Flasks for 24 hours, list them for 2 or 8 hours if you're going to overprice them.
Enchanting can be a decent money maker if you have exotic patterns. Spamming trade chat for hours on end to get 5g tips for enchanting Str to gloves is a waste of time. Non-enchanters and enchanters alike can turn a decent profit from playing the Dust/Shard game on the AH and buy buying cheap blues and greens and disenchanting them to make profit (look for Imbued Netherweave stuff and do uncommon searches for 65-70 items).
And finally, the biggest money maker of them all: patience, prevention and impulsiveness control.
Don't be impatient to sell what you have and be patient when trying to buy the more expensive stuff - you might be able to save a few hundred gold by waiting a day or two for something that you don't even need 'right now'.
Make sure to have a large hoard of raiding consumables/enchanting supplies/gems on a mule and to keep piling up by buying low. Fel Lotus at 10g each because of undercutting? Buy 30 of them. Super Mana Pots at 8g a stack? Buy, buy buy. Don't wait until you're out and be forced to buy your Mana Pots at 12-13g a stack later.
And it's not because it's purple that you "need" it. Buying expensive stuff on the AH (even when it seems cheap) can be a huge waste of money.