Depends on what you mean by 'rich' - $1M, $10M, $1Bn ?

There have been classes of investment visa for people bringing $1M into the country. But then people simply used it to buy a house = $1M in some areas. So then there were requirements that it had to be invested in a business, so people formed a company, bought a house and leased it to themselves.

So the politicians upped the $$ requirement, but that leads to different problems. People with $100M in cash are often not very nice citizens - do you want to give Col Qaddafi, Kim Jung whoever, etc a US visa if they bring $100M of their people's money with them? How many of their family/ friends/ associates also get a visa?