According to IRS.gov, as long as you do not exchange more than $1,000 with the same person in the same day, you do not need to register as a Money Services Business
Businesses that are considered MSBs for registration purposes are those that act in one or more of the following capacities: as an issuer, seller or redeemer of money orders or traveler’s checks; as a provider of check cashing services, or as a currency dealer or exchanger, and conduct more than $1,000 in money services business activity with the same person (in one type of activity) on the same day. In addition, all businesses that provide money transfer services in any amount are considered MSBs and are required to register.http://www.irs.gov/businesses/small/article/0,,id=158384,00.html
As far as I know, staying under this limit should also keep you free of any anti-money laundering registration.
It's unclear as to what is considered a money transfer service, though. My presumption is that a person looking to transfer money to another individual is what is considered a money transfer. As long as it is a single individual only looking to exchange or buy currency with another peer, it should not be considered this.
By these definitions, it should be legal for any single person within the United States to buy/sell/trade Bitcoins as they please as long as they do not sell more than $1000 to a certain individual in one day. Of course, any income would still need to be reported, but you should not require any business registration for peer to peer exchange. Trading markets and exchangers might have it much worse off considering they could be considered a money transfer service.
Someone please correct me if I'm wrong.