Is it possible to stop gold selling?

I believe that it is.

Why does it matter if people can just throw their credit cards at every challenge or aspect of the game?

Well, speaking subjectively, I believe that an MMO should be a virtual world. We should all arrive on equal footings and be cut off from the influence of the real world as much as possible.

Additionally, it is important to have an environment that encourages people to use the tools at their disposal and work co-operatively, instead of throwing mummy or daddy's credit card at it when ever it becomes a little challenging or boring.

Thus, some OCC (Out of Character Chat) words and phrases can possibly be filtered from public / vicinity channels much like vulgar language is handled in many games. Further, I believe that if it is allowed then it robs others of their accomplishments and achievements. There is also how it can change the ambiance of the game from one of "playing the game" to "working the game."

Firstly, one needs to hold the people legally accountable, especially for serious charges. For example:  

"To complete the registering of your account, please print off this form and take it to your local police station. They are to post it with a return address, certifying your identity along with a copy of your passport details."

There is then the problem where some countries are impoverished and corruption is rife.

"Due to the country you live in we have banned all ISPs from connecting to our game servers unless they come from a white listed sub address. One of our verification consultants will be in your [country/city] in the week of ... during the month of ..."

There are a few benefits to this:

• Ensures that your subscribers truly wish to be in your world.
• Sets out a procedure that if not carried out properly results in the breaking of serious laws, such as fraud and bribing officials.
• Slows down the process to make it less financially viable for "gold farming" companies to attempt to re-gain access. Hopefully with needing different anonymizer proxies it would become too expensive.
• More generally, it reassures players that their achievements are fully accomplished and others can't buy or cheat their way there.

How to catch them?

• Accounts
• Banking details 
• Chat logs 
• IP addresses.
  

All MMOs have these and would be crazy not to use them. Here are some lines of thought that might rouse suspicions:

• Why would someone who hadn't spoken much and aren't on each other's friend list, give away say 90% of the wealth on their character to this obvious stranger?
  
• Why would they give away a substantial amount to a stranger that doesn't speak the same language and they hardly talk to each other?
  
• Who gave the sales mule (character made for just one purpose) all those credits?
  
• Why did the IP address of a character change from city to city, states, countries or even continents?
  
• Why did the new IP address user change the language they speak in?
  
• Why did the new player suddenly start making new friends and can't seem to play the same way any more?
  
• How did a group or clan suddenly come into enough wealth to afford a hugely expensive group asset?
  

Why can't characters have their wealth tracked and audited in their transactions to each other?