This is a developing area within the law.
In the United States, 18 U.S.C. § 1030 (Computer Fraud and Abuse Act) governs.
However, the law is broadly written. This means creative prosecutors can and do win federal criminal cases by arguing the law should apply. Whether violating a website's terms of service should be considered a federal crime subject to the Act has been a subject of hot debate.
In United States v. Nosal, 676 F.3d 854 (9th Cir. 2012), the 9th Circuit decided violations of use should be considered breaches rather than crimes. However, the district court refused to dismiss some charges against Nosal when the case was returned, and a jury conviction resulted in a prison sentence.
At least three different circuits have arrived at other interpretations of the CFAA. Draft legislation (H.R. 2454 and S. 1196) would limit the scope of the CFAA by excluding TOS violations, however, it hasn't been adopted as of this writing.
That CAPTCHA breaking violates website terms of service isn't really in question. For example, see U.S. v. Lowson, 10-cr-114, U.S. District Court, District of New Jersey (Newark) in which the judge brought a criminal case to which two defendants plead guilty to wire fraud, one plead guilty to misdemeanor computer crimes, and a fourth went on the lam.
But does for-profit CAPTCHA solving violate U.S. law? Given the state of the law, one could make a case either way. Given the industry's reputation, serious questions about intended use, and questionable labor practices, that's a significant risk.