I have tested a lot and here are the best places to farm for gold in Diablo 3.
Fields of Slaugther
Fields of Slaugther is in my opinion by far the best place to farm. With Diablo 3 moving away from boss runs for loot, farming has become a question of how to kill the most monsters in the least amount of time. Any monster can potentially drop a legendary and while champion mobs and special monsters are good, normal monsters should not be discarded as they are fast and easy to kill.
Fields of Slaugther is great because it has both a high density of normal monsters to kill and a good chance of multiple rare and champion packs to spawn.
It is also the best farming place in D3 because there is a very good chance of finding the Cavern of Frost which has champion and named monsters and a Resplendent Chest in the bottom. I also often find a Treasure Gnome in the Cavern of Frost giving me even more drops and gold.
The Fields of Slaughter are even a fantastic farming place in Inferno. You know those Demonic Mines that has a tendency to kill you when you are mindlessly grinding away? Yeah well, they can be used for killing off mobs too. Just kite the monster across the mines and watch them take almost a million points of damage when the Demonic Mine explode.
Finally it is awesome for solo farming, because not only do you get your follower, Tyrael will join you in the battle as well.
To get to the Fields of Slaugther, simply pick Act 3 and the quest the Siegebreaker.
Now just clear the area, find the the cave and then reset and go again.
Whimsyshire
Whimsyshire is a great place to farm for items, although not as much for gold. The drop rate of blues and Yellows in Whimsyshire is incredibly high, even with little Magic Find. The drawback of course is the cost to get access to Rainbowland. 150k for the normal staff of herding, 200k gold on top of that for access on Nightmare. Hell will cost you 500k gold and the Inferno Whimsyshire staff is a staggering 1 million gold, meaning you will have spent 1 million 850k gold for your farm place. Of course if you are lucky and get a legendary drop amongst all the blues and yellows, that will easily cover your entrance fee. Time to gamble on the drop rate perhaps?
Garden of Hope level 2 and the Silver Spire
These levels of Heaven are okay in terms of gold drops, but not as good as the Fields of Slaugther. They are however better if you want to get some high level drops.
Gardens of Hope and the Silver Spire is good because there are a lot of monsters spawning. The drawback is that the monsters here are quite hard and as such you chance getting killed over slightly better loot. In terms of time vs payout for farming I don't feel the increase in gold and items over act 3 is worth it.
Personally I would recommend Fields of Slaugther for Gold and the Whimsyshire for items, but if you do not have access to the latter or you want to farm for both at the same time, then the Silver Spire and Garden of Hope are going to fit the bill.
The most important thing in terms of picking a farming spot in Diablo is to look for high density "easy" to kill monsters with high drop rates. The less you have to move and the more rares/champions or chests you have access to in the area the better.

as people go through the content I foresee the normal mode crafting materials becoming really cheap or not selling at all. At this point in time you can still sell them, however here is a small tip. The subtle essence sells for between 20 and 25 gold per item at present and the Fallen Horns are about 40g (This is likely to fall drastically). Most blue items of act 3-4 sells for 100+ gold and you usually only get 1 essence or horn from an item. This means that unless the item value to sell to a merchant is less than 30 I would not recommend salvaging from a pure money perspective.
The same goes for Shimmering essence and Lizard Eye with prices on the auction house 30g and 150g. Most items simply sell better to the merchants.
There will be plenty of
people buying gold, items, dyes and recipes. Especially if the PvP
part of Diablo becomes succesful, but even if it is only moderately
good, people will buy, shop, purchase and all the other lovely words
merchants like us love to hear. And best of all, this time around it
will be legal for players to go through with these sales and a
supported system created by Blizzard themselves to sort out the
sales. This means people who were previously too scared to get
scammed will also start buying items for real money.