Method acting as a concept has been around since the 1930s, derived from Stanislavski's system (predating the former by a few decades) of actors creating 'real' emotions by Meisner, Adler and Lewis.
Though it has evolved slightly over time, the core component is that the actor employing the technique of method acting 'becomes' the character they're playing by taking the (either hypothetical or explicit) psychological and emotional motivations of the character and making them their own.
Actors utilizing the techniques promoted by Stanislavski, Meisner, Adler or Lewis include: Marlon Brando, Robert DeNiro, Al Pacino, Daniel Day Lewis, Meryl Streep, Marilyn Monroe, etc. etc.
Is there any correlation between using these techniques and success (success being measured by awards, box office tallies, long career)?