The American Cancer Society has a good overview of the scientific evidence:
Available scientific evidence does not support claims that Laetrile or amygdalin is effective in treating cancer or any other disease. Both contain a small amount of a substance that can be converted to cyanide in the body, and several cases of cyanide poisoning have been linked to the use of Laetrile. The U.S. Food and Drug Administration (FDA) has not approved Laetrile as a medical treatment in the United States.
[A] 1991 review notes that, beginning in 1957, Laetrile was repeatedly tested against tumor cells implanted in animals. At least a dozen separate sets of experiments were done at seven institutions. Targets included several different types of cancer. The conclusion was that Laetrile did not have any anti-tumor activity.
The FDA placed sanctions against the sale of Laetrile. In 1977, the FDA commissioner stated that there was no evidence for the safety or effectiveness of Laetrile. Because of the risk of cyanide poisoning, the government has banned the transport of Laetrile into the United States or across state lines, as well as the use of Laetrile in states without laws specifically allowing it. Since 2000, there have been several instances of prosecution because of Laetrile transport across state lines. Nonetheless, products advertised as Laetrile and amygdalin can still be purchased via many websites.