From this site
, harboring a fugitive means to knowingly hide a wanted criminal from the authorities. Different authorities are going to have slightly different definitions of what behavior it takes in order to be guilty of the crime of harboring.
There are several U.S. federal statutes that cover harboring and flight from prosecution, in Chapter 49 of Title 18 of the United States Code
. 18 USC 1071 is the most relevant to your question and reads as follows:
Whoever harbors or conceals any person for whose arrest a warrant or process has been issued under the provisions of any law of the United States, so as to prevent his discovery and arrest, after notice or knowledge of the fact that a warrant or process has been issued for the apprehension of such person, shall be fined under this title or imprisoned not more than one year, or both; except that if the warrant or process issued on a charge of felony, or after conviction of such person of any offense, the punishment shall be a fine under this title, or imprisonment for not more than five years, or both.
So, in the U.S. federal criminal system, there are four elements that need to be satisfied in order to be guilty of 'concealing a person from arrest':
(1) proof that a federal warrant had been issued for the fugitive' s arrest,
(2) that the accused had knowledge that a warrant had been issued,
(3) that the accused actually harbored or concealed the fugitive, and
(4) that the accused intended to prevent the fugitive' s discovery or arrest.
Here's a link to the U.S. federal government's Criminal Resource Manual
explaining each of the elements of the statute, with cited caselaw indicating what an AUSA needs to show for each element. (The link takes you to a page explaining the first element. Click 'Next' to get each element after that.)
Finally, here is a link to U.S. v. Hill
, 279 F.3d 731 (9th Cir. 2001), which explains, eventually, that section 1071 has extraterritorial application. (Scroll down to Section II B. 2) Now, as to what the laws were at the time of the Godfather, I've no idea.