The Mutant Registration Act is a fictional law that required all mutants to register with the government.  It was first mentioned in the Uncanny X-men #141  when Moria MacTaggert suggest that Senator Robert Kelly has suggested that mutants must be registered under law by the government.  The law does eventually go under way and is made clear when Senator Kelly is discussing  the introduction of the law with a colleague. Later, in Uncanny X-men# 183 the Act is made as a passed legalisation and in 188# it becomes an accepted law. 
 
The Mutant Registration Act did not have any major impact on the story lines in the Marvel Comics, but it was part of some of the plots. This law is what motivated Cyclops and Jean Grey to form the original X-Factor group and it was one of the reasons Valerie Cooper and Mystique formed the Freedom Force.