Final answer:
Carl Rogers' client-centered therapy has had the most lasting influence on psychological therapy due to its focus on empathy, unconditional positive regard, and empowerment of the client, which have become core aspects of many therapeutic practices.
Step-by-step explanation:
Of the three approaches to psychological therapy—Freudian psychoanalysis, Carl Rogers' humanistic therapy, and behavioral therapy—the humanistic approach, notably Carl Rogers' client-centered therapy, is widely regarded as having the most lasting influence on psychological therapy to date. Sigmund Freud's psychoanalysis has been monumental in introducing concepts of the unconscious and childhood experiences in shaping behavior, which are still integral to some forms of modern therapy.
However, criticisms related to its scientific rigor have somewhat diminished its prevalence. On the other hand, behavioral therapy, with its focus on observable behaviors and the impact of the environment on behavior as proposed by B. F. Skinner and Albert Bandura, has been foundational in developing empirically supported treatments.
Yet it is the client-centered approach, also known as person-centered therapy, which has become incredibly influential in the therapeutic landscape due to its emphasis on empathy, unconditional positive regard, genuineness, and viewing the client as capable of self-healing and personal growth. These principles have been integrated into a wide variety of therapeutic practices, emphasizing the therapeutic relationship and the empowerment of the client.