From a growth perspective, the goal of therapy is not just to "get back to normal" but to learn something about ourselves that allows us to grow as individuals. The assumption is that growth occurs naturally over the lifetime, and it is an inherently positive process. Many people seek therapy with a goal of "growing", often because they feel that other parts of their life (e.g., peers, family, or their environment) are not supportive of their growth.
These two categories overlap, of course. Investigating and shifting out of age-old patterns that developed early in life and that still produce problems in our lives can be looked at either as a way to address problems (or "symptoms") or as promoting our growth. If the therapeutic work leads to positive subjective change or improved objective functioning, it doesn't matter what motivated it.
All that said, each therapeutic perspective - Ego psychology, Lacan, Gestalt, Self psychology, for example - have different views of the "goal" and this can radically influence the nature of the therapy. Meanwhile, each therapist comes with his or her own idea of what the goal is, even within the same clinical perspective.
All this is to say that, as I investigate different approaches, I've been keeping my eye out for what each writer considers the "goal" or "purpose" of therapy, to get a hint about each one's overall attitude towards life, individual autonomy, and human relations.
As one example, Gestalt therapy views many problems that people come to therapy with as growing out of the inability of the individual to adapt to his or her ever-changing environment. Here is quote from Perls' The Gestalt Approach that summarizes his vision of the "goal of psychotherapy" (apologies in advance for the dated pronoun usage):
The man who can live in concernful contact with his society, neither being swallowed up by it nor withdrawing from it completely, is the well-integrated man. He is self-supportive because he understands the relationship between himself and his society, as the parts of the body instinctively seem to understand their relationship to the body-as-a-whole. He is the man who recognizes the contact boundary between himself and his society, who renders unto Caesar the things that are Caesar's and retains for himself those things that are his own. The goal of psychotherapy is to create just such men. (p. 26)As I come across other statements by different theorists, I will post them, and perhaps contrast them.