Farming gold in Diablo 3

Solution 1:

THIS ANSWER IS CURRENT AS OF PATCH 2.0/REAPER OF SOULS

The answer to this question is now a lot simpler than it was when the Auction House was around, and different difficulties were more ambiguous about their effects. Now you can increase your gold per hour in THREE primary ways:

Bounties and Nephalem rifts

After completing Act V, you will unlock access to Adventure mode, which will allow you to undertake bounties and occasionally Nephalem Rifts. In each of these modes, you are given a specific task to undertake in certain parts of the game, usually killing a certain mob or clearing an area. Once you do that, you are rewarded a substantial sum of XP and gold, in addition to any that you earn along the way by killing mobs or completing a side quest like a cursed chest. In Nephalem rifts, particularly, mobs come fast and furious which create ideal conditions for lots of gold drops.

Raise the difficulty

The higher the difficulty, the more gold will drop. However, it is up to you to find the sweet spot between what difficulty allows you to move quick enough to make the bonus worthwhile. i.e. is it better for you to run 4 bounties per hour on Torment I or 6 per hour on Master?

Normal Enemies have 100% health, do 100% damage. No XP or gold drop bonuses.
Hard Enemies have 200% health, do 130% damage. XP gains and gold drops both boosted by 75%.
Expert Enemies have 320% health, do 189% damage. XP gains and gold drops both boosted by 100%.
Master Enemies have 512% health, do 273% damage. XP gains and gold drops both boosted by 200%.
Torment I Enemies have 819% health, do 396% damage. XP gains and gold drops both boosted by 300%.
Torment II Enemies have 1,311% health, do 575% damage. XP gains and gold drops both boosted by 400%.
Torment III Enemies have 2,097% health, do 833% damage. XP gains and gold drops both boosted by 550%.
Torment IV Enemies have 3,355% health, do 1,208% damage. XP gains and gold drops both boosted by 800%.
Torment V Enemies have 5,369% health, do 1,752% damage. XP gains and gold drops both boosted by 1,150%.
Torment VI Enemies have 8,590% health, do 2,540% damage. XP gains and gold drops both boosted by 1,600%.

The table above comes from this site.

Increase your gold find percentage

As in vanilla D3, increasing your gold find stats will provide an increase to the amount of gold dropped. You should balance this, however, with finding gear that makes you more effective at killing mobs, thereby increasing your throughput. Luckily, on most gear, gold find is considered a "secondary stat" and does not take away from primary skills like dexterity or crit chance. You'll need to find your own balance of quantity of kills vs. quality of kills.

You can also increase your gold find through the Paragon leveling system. Keep in mind, as above, you'll be taking points from other areas that might make you more effective in combat, such as "life on hit". But this is a good way to increase your gold find without finding specialized gear. Since you can reset paragon points at will, this may be a good way to increase gold find on difficulties where you don't need the other utility stats.

Solution 2:

To get pure gold the two biggest factors are how much gold find you have and what act/difficulty you are in(higher is better untill you reach Inferno where Act wont matter). The key facter here is balancing the amount of gold find you have so you can still kill high level monsters. You can also make a pure gold find set(also works for magic find) and after clearing an area for monsters equip your set and go open chests and destroying things that can contain gold/items.

But a better way of getting gold is using the AH, there is no cost to putting items up and there are plenty of people buying items, atm I would recommend focusing on magic and rare level 45-59 weapons with high dps and high damage stats(str/dex/int), but other items with good stats also work. The reason for the level is that people need to be high enough to have gold, and once you hit 60 it is a lot harder farming for the easy selling items (higher standards). Don't be to greedy, it is better to sell a lot of items at a lower price than a few at high, if you can sell 5 weapons at 50k each you will make more than selling 1 at 200k in the same period. Just try and make sure to always use the 10 item slots you can have up on AH.

Solution 3:

Stockpile gear with Gold Finding stats on it so that your Gold Find is high (you can view this under Character Sheet->Gold Find.

You then have some choices. The higher difficulty mobs, as well as higher Act mobs, drop more gold then their predecessor. However, they get tougher to kill, taking longer.

I have no proof of this, but it seems to me that Act III is the best Act to farm anything - gold, XP, items, etc. because it appears to me to have the most amount of mobs that are still somewhat squishy.

If you are really looking to farm, I'd recommend Act III of the highest difficulty that you can do, and as others mentioned, don't just focus on pure gold drops; items can sell very well in the AH.

And remember that not only rares have great stats! A magic (blue) item can carry the best stats in the game.

Here's an official blue post stating so:

Legendary items are commonly not going to be the best items. It's a title that denotes a named item, with set stats, and a unique model. It does not mean they're the best items.

Completely random rares will be the best items in the game if they roll up the right stats.