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With your typical MMORPG, players can usually farm the world for raw materials essentially forever. Monsters/mineral veins/etc are usually on some sort of respawn timer, so other than time there really isn't a good way to limit the amount of new currency entering the system.
That really only leaves money sinks to try to take money out of the system. What are some strategies to prevent inflation of the in-game currency?
Entropia Universe uses the real green stuff, as players deposit IRL money which they can later withdraw, so inflation needs to be kept in check -- otherwise the whole company may bankrupt in an instant. The solution for Entropia Universe is to forge new items with an average value < the average value spent to create/obtain the items. This is the same type of system you find in gambling: ROI < 1:1. (The surplus pays for development and owner dividends.)
If you run with this in a normal game (without IRL cash) you need to keep track of the total value in the system. Then you ("the Treasury") can choose when you need/want to create more value in the game, or do so automatically if the value drops below a certain threshold.
Many answers have hit on the essentials as far as limiting the INPUT i.e. do not allow infinite gold creation, infinite monster and material respawn based on simple timers, etc. Gold should circulate. Monsters should have loot because they got it from somewhere. Players who die in a dungeon could lose cash, that then ends up in the pockets of monsters that can then be killed by other players, etc. The point is to do everything possible to increase circulation, but limit spawning of currency out of nowhere.
One very interesting area that provided a lot of inspiration to me is to look at how historic economies actually worked. I like the fantasy genre, so I studied medieval economics. There were actually many highly efficient "gold sinks" built into most medieval economies. For example, guilds would have to buy royal charters from the king in order to operate. They would control the ability to allow (for example) blacksmiths to operate in a given area, but in turn, they would have to pay a bunch of money to the king for a "charter" that gave them that authority. This mechanic in an MMOG would allow for A: creation of local monopolies that would be a natural source of conflict between players seeking to control it (conflict is good if you channel it into game activity), B: Player arbitrage activity as they buy stuff in one location and move it to another (assuming you don't have instant, free, fast travel), and C: An efficient gold sink that allows the game developer to target a very specific industry. You can get some pretty fine grained control over exactly where you want to suck excess currency out of the economy by adjusting charter prices for blacksmiths versus bakers versus tanners.
There are a lot of simple solutions to economic problems (some of which create other problems of their own) to be found in historic economics. It does make a lot of sense for a fantasy game to implement some of them, because no only do they allow for band aid fixes, but the "flavor" element of having a mechanic like royal charters actually adds to the game, rather than feeling like an arbitrary, punitive mechanic.
We can go for one problem that creates the inflation:
The theoretical amount of money in trade in the entire MMO is infinite, because the input stream of monsters and quests can be infinitely done.
A shortcut fix would be to find places were money leaves the active economy without any return. That could be anything from paying money for re-spawn(probably the most unlikely) or something like a consumable item (so it can't go into endless trade) that costs a high amount of money.
You can instead opt to prevent the negative influences of inflation, while otherwise taking advantage of it. To do this you must make the market very accessible. Rather than relying on item clutter as a sink, drop only useful items that will be great hand-me-downs, upgrades or crafting components.
Where pragmatic, make drops slightly rare and prefer gold. Track inflation for equipment and items of all level/skill tiers, defining a ratio to the game's original value-balance.
Use this multiplier from the active market against gold drop rates. By doing this and restricting price changes to within + or - 40% within a given time, and increasingly discounted under market value for greater quantities of an item. Only allow price increases for small stacks (the size of an hour of drops/crafting) or HQ items. This way you provide players with a consistent financial-progress experience.
So, now that you've ensured a player can go grind and get obtain nice gear with a fair but not insane amount of effort, you can refine more market activity from there.
Detect trends within the market data gathered to track inflation. Give NPC guilds the ability to create items, given a combination of drops or money, as player crafters would. Then let them buy up underpriced items relative to how much cheap surplus is flooding an item's market. NPC activity can and should work at similar multiplier to player economy, making slightly less profit at a worse overhead than players (about 20-40% less efficient at profiteering is good). "Use" that profit to actually fund NPC salaries and activity. If NPC teams/armies can only move when they have enough gear, food, salary and recruits, the game can be quite dynamic from some simple self-balancing mechanics.
With a rough equilibrium formed, and as the game admin, you can play around with both inflation and deflation with temporary, gradient shifts in various ratios.
Another way to let both players and NPCs take advantage and self-adjust to inflation is through loans. Imagine a cursed ring of lending. Monetary activity is taxed until repayment, plus interest of course. If players can take out a substantial mortgage based on their average rate of earnings, and drops scale up with inflation as above, players can suddenly pay off their debts.
Ah, but you can measure the total inflation volatility, and pack that into the interest rates and transaction fees in various ways. Even go so far as to have various levels of tribes to governments take on massive debt and properly collapse, to suck tremendous amounts of gold out of the economy as needed.
Options are endless, but I'll provide one more. The most direct method of straight up deflating the economy is to really push the NPC involvement in player markets. Specifically, if:
Actually failing game economies are as much about basic math as a direct result of social ineptitude.
The recycle-ability of things abroad, in-game or out-game is relatively the same. Massively people are used to doing whatever they are doing and leaving a humongous mess in their wake. These thought patterns directly go through designers making games. Where the world outside of games forces you to engage in a broken and heavily rigged economy just so you can obtain food, shelter and more. For a game and its economy you can simply walk away and spare your self the useless grind. You are at a grindy job with decreasing benefit any way, riding griffins in some game context isn't going to be awesome if you are subjected to the same economical torture you endure in your daily life.
Likewise overcompensating for this factor leads to absurd levels of inflation and abuse that quickly tears down any fun provided by the game environment. Not to mention technical issues resulting in exploits and such. And not even considering the hardest element of planning - efficiency variables - having an absolute best way to play the economy that usually renders most other gameplay activities useless, as players couldn't keep up with those "playing" efficiently.
The problems we are experiencing largely in the world today, play out numerously in games with economies. As they are built upon the same outdated and heavily faulty presumptions. except in games, the small scope and size of these projects reveals these flaws much faster than we get to comprehend them in the world we live in outside of games.
Overall most developers have economies for the same reasons a new car manufacturer puts tires on their cars. "Everybody else has them and the concept wouldn't work without them." However we all know the majority of manufacturers wouldn't go as far as to improve upon tires in any meaningful way or have any idea how to go about it even if they wanted to. That is IF their goals and budget have even considered tire improvements at all.
Why do economies fail? Because the people who make them lack the bare minimum of understanding. Its one thing to be in an economy as a participant. Its an entirely different thing to have the control over creating an economy and still fail in the end.
A lot of designers and devs I've spoken said to lack even basic projections for their economies. I know plenty who entirely "eyeball" their costs, times and so on. There are people who make large scale games and approach economy in a mystical fashion that, they can just set out and throw a bunch of whimsical random data that looks good on the eye and expect that it would "somehow" magically align to self-sustainability in the end. I also know people who do it on purpose. Here is a copy paste conversation from one of them I talked to just the other day:
"My boss wants me to design every feature, help with QA, babysit CMs more or less manage the coders, if he think I'm going to do the work of an expert mathematician and integrate it into the game in a way that makes sense, someone is gravely mistaken and its not me. I've insisted that either the scope is scaled back to fit what we can do, or more is invested to do it properly. Both were rejected, because the decision makers care more about appearing authoritative than actually understanding what is happening in their project. So congratulations, keep the payroll flowing and ask me create a new txt file type some random stuff in and then delete it, I'll repeat 24/7 if you insist - I don't care any more. When i go looking for a new job, it will be fine, I strictly followed my tasks, integrated with co-workers well, met my deadlines good enough, if anybody asks i sure as hell didn't make the economy, in fact i have an old email proving I have foreseen most of the problmes, not my problem that management ignored it. You know they never believe you when you say you didn't have enough to work with, considering we are in the crunch time industry, which is supreme at dehumanizing people with passion and potential about making games. Why do you think some of those cool profitable indies made it solo. Most of them begged companies to look at them and throw them a used bone, except corp scale devs could have bought them for pennies but instead threw em out flat on their ass because they are utterly incompetent at recognizing potential. They wouldn't even ship out their own games in a playable manner what do you expect?"