Craig Keener, in his excellent commentary on Matthew, says "more than thirty-six discrete views exist" on the Sermon on the Mount.
He quotes Blomberg (1992) summarizing the most critical of these:
The predominant medieval view, reserving a higher ethic for clergy, especially in monastic orders;
Luther's view that the sermon represents an impossible demand like the law;
The Anabaptist view, which applies the teachings literally for the civil sphere;
The traditional liberal social gospel position;
Existentialist interpreters' application of the sermon's specific moral demands as a more general challenge to decision;
Schweitzer's view that the sermon embodies an interim ethic rooted in the mistaken expectation of imminent eschatology;
The traditional dispensational application to a future millennial kingdom; and
Blomberg's and others' view of an "inaugurated eschatology", "in which the sermon's ethic remains the ideal or goal... but which will never be fully realized until the consummation of the kingdom..."