In a detailed article, ArsTechnica looks at whether or not the RIAA could be tried under the RICO statutes that have typically been used to prosecute organized crime.
And the conclusion:
At the end of the day, the RIAA may be a lot of things, but a criminal enterprise engaged in racketeering is not one of them. Federal law gives copyright holders the ability to seek recompense via the court system via civil cases, and that's what the RIAA is doing. Atlantic v. Andersen is still making its way through the courts, and the judge has yet to rule on Andersen's counterclaim, including the RICO allegations.