There are many lasting legacies of MLK and the civil rights movement generally, but I think there's one which seems to get less attention than the others - the Voting Rights Act. Some parts of it are only as good as the attorney general who is enforcing it, but at the very least it began the process of ending a whole host of measures designed to prevent a sizeable portion of the populations of many states from voting.
1965 was less than 40 years ago, and at that time in much of the country African-Americans could not vote.