I cannot believe that the purpose of life is to be “happy.” I think the purpose of life is to be useful, to be responsible, to be honorable, to be compassionate. It is, above all, to matter: to count, to stand for something, to have made some difference that you lived at all.

Leo C. Rosten (1908-1997) Polish-American author and political scientist

“Credo,” Passions and Prejudices (1978)
    (Source)

This appears to be the final iteration of a thought that Rosen used on numerous occasions. In "On Finding Truth: Abandon the Strait Jacket of Conformity," Speech, National Book Awards, New York City, as reprinted in The Sunday Star (8 Apr 1962):

The purpose of life is not to be happy -- but to matter, to be productive, to be useful, to have it make some difference that you lived at all.

In a later essay, "Words To Live By: The Real Reason For Being Alive," This Week Magazine (20 Jan 1963):

THE PURPOSE OF LIFE is not to be happy. The purpose of life is to matter, to be productive, to have it make some difference that you lived at all. Happiness, in the ancient, noble sense, means self-fulfillment — and is given to those who use to the fullest whatever talents God or luck or fate bestowed upon them. Happiness, to me, lies in stretching, to the farthest boundaries of which we are capable, the resources of the mind and heart.

In "The Myths by Which We Live," The Rotarian (Sep 1965):

Finally there is the myth which gives me the greatest pain: the myth that the purpose of life is happiness, and that you ought to have fun, and that your children ought to have fun. Where was it written that life is so cheap? Where was it written that life is, or should be, or can ever be free of conflict and effort and deprivation and sacrifice? [...] [T]he purpose of life is not to be happy at all. It is to be useful, to be honorable. It is to be compassionate. It is to matter, to have it make some difference that you lived.

A variation of this quotation is misattributed to Ralph Waldo Emerson. More discussion of this quotation (including a shout-out to WIST for some of this research) here: The Purpose of Life Is Not To Be Happy But To Matter – Quote Investigator.