It's important to differentiate between a scam, where a person or entity stands to profit fraudulently from others, and a high-risk investing decision, where there is potential for a person to lose significant amounts of money without being defrauded by anyone. With that clarification, Bitcoin is clearly not a scam. Like any other currency, Bitcoin is designed to be used as money, not as an investment.
A Ponzi scheme is a type of confidence scam where people who think they are earning unusually high returns on an investment are actually being paid from their own money and that of later investors. If investors try and withdraw their original investment from the Ponzi operator, the scheme collapses because no actual profits exist and there is not enough money to return the deposited amounts. Alternatively the Ponzi operator may simply leave and take the investors' money with them.
Similarly, a pyramid scheme is a type of confidence scam where people who "enroll" by paying a certain amount of money are made to believe they can make a large return on their investment by recruiting other people and receiving some portion of their enrollment fee. The scheme collapses because it requires exponential growth, so it quickly runs out of new people to enroll. The person starting the pyramid scam, who didn't have to pay an enrollment fee, makes money off of all their referrals; while the people at the bottom parts of the pyramid, who cannot find anyone new to refer, are left with no return.
Unlike either of these situations, Bitcoin has no person "at the top" who collects money paid for bitcoins, or has to pay out when bitcoins are sold. Neither is there any kind of scheme in Bitcoin to harvest money off of unsuspecting people in complicated ways. Instead, bitcoins are bought and sold on public exchanges amongst members of the general public who must all obey the same rules. If someone has told you that Bitcoin is a moneymaking scheme, they have misconstrued it--bitcoins follow the same economic model as any other finite commodity and over time will tend to approach a price that reflects the value people ascribe to being able to use them. People who have made money off of buying and/or selling bitcoins are either lucky or have correctly predicted an increase in demand for them. People who earn bitcoins through "mining" are being paid for verifying and securing network transactions in a highly competitive market. In neither case is any kind of fraudulent activity or confidence scam happening.
Despite the fact that Bitcoin itself is not a scam, caution is strongly advised when entering into transactions with untrusted entities. As with any other valuable commodity, there are many people willing to separate your bitcoins from you in sneaky or fraudulent ways. Remember that for all practical purposes Bitcoin works just like cash. Bitcoin Ponzi and pyramid schemes do exist and if you fall prey to them you will suffer the consequences.
In addition, bitcoins are a very new and unproven type of money. Because their value depends on how widely they are accepted, they are susceptible to the same types of economic bubbles as any other commodity that is surging in popularity. The Bitcoin software is still in beta, and bitcoins should be considered "high-risk" from a financial perspective. You should not invest money into bitcoins or Bitcoin-related technologies unless you can afford to lose it! Even firm believers in Bitcoin tend to think it will take a while for the value of bitcoins to stabilise, and no one knows at what value that stabilisation might occur. Trade and transact safely!
Adam Cohen later retracted his allegation of it being a scam, which is mentioned at the end of his answer:
"Update 6/2: For those of you also on Hacker News, I made a couple of clarifying points, which included an apology for glibly using the word scam. Read more here.
Open source software can obviously not be a scam, since it has no agency, and due to its licensing, cannot be owned by any party with agency.
The most that can be alleged is that someone created an open source program in order to conduct a scam, or that someone is using the software as part of a scam.
In the case of Bitcoin's creator, the pseudonymous Satoshi Nakamoto, his purpose in creating Bitcoin was clearly to effect political and economic change -as evidenced by what he writes in his white paper and in the mailing list through which he communicated about it before and shortly after the release of the software- and not to personally profit.
As for the criticism of it being a ponzi scheme, it's not true by definition. A ponzi scheme is structured so that those who join the scheme later give money to those who joined earlier, and nothing else is traded.
There is only one possible outcome in a ponzi scheme, and that that the early adopters profit, and the later adopters have membership in a ponzi scheme that they paid into but that they cannot profit from.
For any asset like Bitcoin, or a company stock, the early adopters will profit in the event of appreciation, but there is something of underlying value that all adopters will have if it succeeds. In the case of Bitcoin, it is a currency that can be used in trade as a medium of exchange, allowing for a reduction in transaction costs and an increase in transaction speed and convenience, and providing a store of wealth that doesn't depreciate due to inflation.
Bitcoin by itself is a protocol. It is not an investment nor does it make any claims that you will get a financial return for using it.
Bitcoin is definitely not a scam. People have opinions about whether it will or will not succeed, but it's not a scam. It like to think of it as the first money that is designed for the internet. There have been previous attempts at digital money, but all have relied on a central authority to solve the "double spend" problem. Until the advent of bitcoin, a transaction on the internet required a third party to the transaction (for example, a bank that manages account balances). Bitcoin, like cash, requires no third party. Also like cash, it is an irreversible transaction and can be stolen. Bitcoin was designed with the modern internet in mind unlike credit cards (invented in the 1950s) or ACH (invented in 1972). Bitcoin can serve as a solid (as in secure) foundation on which many other financial instruments and innovations can be based. The software systems that the current banking system uses are antiquated, haphazardly put together, and could not have foreseen the needs of the modern internet.
A lot of people state that no claims are made that you will earn a financial return. That may be true, but manufacturers certainly imply that you will earn money. Why else would they charge thousands of dollars for mining hardware?
I think your question is fair, because there are calculators out there that predict a user will never earn-back the $5K they spend on expensive mining hardware, especially when said hardware won't arrive until Spring of 2014 (when difficulty has increased dramatically by then). Still, any time you question the manufacturer on an unrealistic price, they hide behind the aforementioned claim that they "can't predict market activity" and that you should purchase their equipment "at your own risk".
It's just a new method of conducting transactions, similar to paypal but impossible to reverse transactions. People who don't understand it call it a scam, but it is not.