WHEN Irving Berlin wrote "There's No Business Like Show Business," he certainly didn't have book publishers in mind. Yet, as it turns out, he might as well have.Books about the entertainment industry have become popular publishers' staples. Movies and television have reached that ripe old age where nostalgia is rampant. And readers seem to have developed a fascination for the ups and downs of the business itself. In a wide variety of recently published show-business books, past and present meet, and often complement one another. Here is a selection of some of the most interesting. Me: Stories of My Life, by Katharine Hepburn (Alfred A. Knopf, 420 pp., $25), is probably as authentic and appealing as autobiographies get. "Me" catches all Miss Hepburn's wonderful, refreshing qualities - her straightforward honesty, her clear-eyed view of people, her capacity to attract friendship and love, her unwillingness to compro- mise, her basic decency, and her headstrong - often selfish - determination to succeed. The actress relates her youth and upper-class New England upbringing, a burning ambition to become a star, adventures, her marriage and subsequent affairs - including years with Howard Hughes and, of course, the romantic, utterly discreet, 27-year link with (the married) Spencer Tracy. The chapter on Hepburn's relationship with Tracy is aptly headed "Love." In it she provides hints of how tender and supportive it was. In her inimitable style, she provides a moving sense of her complete devotion to the only man she really loved. "Me" is a wonderfully open and discursive book about a woman who, in older years, can afford to look back on her life, her work (four Oscars), her family, her lovers, and her many friends with the disarming - at times almost dispassionate - honesty that seems to have characterized her entire career. A Terrible Liar: A Memoir, by Hume Cronyn (Morrow, 431 pp., $23), is a thoroughly charming, witty, and often funny autobiography not only because it represents a splendid piece of writing, or because of the absence of jarring personal "revelations," but mainly because Cronyn emerges as such a decent, intelligent, fair, sensitive, and likeable human being. What a life he has lived - full of curiosity, experiment, love, and a grand passion for his acting profession. Because Cronyn's writing matches his acting talents, he's able to express life experiences and thought beyond just "the facts." The memoir is filled with color, emotion, self-examination, astute observations of the people close to him (including Jessica Tandy, his wife of 50 years and his costar in so many plays and movies) and a kind of wry, self-deprecating humor that is enormously appealing. The book easily combines personal stories, comments, and happenings onstage and offstage. The description of his courtship of Miss Tandy is touching, and so are the tales of his Canadian youth. Anecdote piles on anecdote as Cronyn recalls working with screen greats like Spencer Tracy, Elizabeth Taylor and Richard Burton (on "Cleopatra"), Laurence Olivier, and of course a host of movie and stage directors such as Alfred Hitchcock and Elia Kazan. Ginger: My Story, by Ginger Rogers (HarperCollins, 450 pp., $22). Think of Ginger Rogers and what inevitably comes to mind are her fabulous, graceful, and romantic dance scenes with Fred Astaire in such great old movies as "Top Hat," "Swing Time," and "Shall We Dance." This autobiography vividly details her life and career - from vaudeville beginnings through her rapid rise to great stardom, a successful transition from dancer to serious actress (she won an Oscar for "Kitty Foyle"), many stage appearances, five husbands, affairs with Hollywood's rich and famous (among them Cary Grant and Howard Hughes), her close relationship with her mother, Lela, who shaped her enduring attachment to Christian Science, and her professional contacts and experiences. Rogers is a first-rate storyteller and paints quite a revealing picture of life, glamour, and ethics among the Hollywood greats during the '30s, '40s, and '50s. What's disappointing is the book's lack of depth. It's mostly on the level of amusing chatter with little effort to convey serious thought. Backstory 2: Interviews with Screenwriters of the 1940s and 1950s, edited and introduced by Pat McGilligan (U. of California Press, 417 pp., $29.95) is the kind of "oral history" we rarely get from Hollywood, and it deals with a group of creators whose vital contribution to the medium is often undervalued. In editing interviews with 14 screenwriters active during the '40s and '50s, MacGilligan etches very distinctive portraits of some of the outstanding men and women scriptwriters and their working involvement with many of the famous films and filmmakers of that turbulent era. There was the war, of course, which brought out some of the best and some of the worst in Hollywood. Then came the communist witch hunts of the '40s and '50s, which had a profound impact on the production community. It's all very accurately, colorfully, and often amusingly reflected in "Backstory 2." Great movie-writing talents like Leigh Brackett, Richard Brooks, Betty Comden and Adolph Green, Garson Kanin, Dorothy Kingsley, Philip Yordan, Curt Siodmak, Arthur Laurents, and others reminisce and explain, prodded by intelligent questioners. The interviews cover a long list of famous movie actors and directors and their essential involvement in the most elemental process of moviemaking - the forging of the script before and during production. Many of them are witty, clever, sophisticated people, and their comments and stories go a long way in explaining what thoughts and logic shaped the movies of that period. Woody Allen, by Eric Lax (Alfred A. Knopf, 386 pp., $24), is an expertly written, and intricately analytical biography about one of today's most versatile, sensitive, and thoughtful artists and humorists. Little has been written about Woody, a very private person who shuns the limelight, so Lax's expert combination of both a critical and personal evaluation of Allen is doubly welcome and a major contribution to the understanding and appreciation of this complicated, multifaceted, hugely innovative, and w ide-ranging talent. A good read! Jean Renoir: A Life in Pictures, by Celia Bertin (Johns Hopkins University Press, 403 pp., $29.95). "I have something really ridiculous to tell you - the arrival of a second son, named Jean," painter Auguste Renoir wrote to a friend in September of 1894. That somewhat tenuous note continued during Jean's early years, which were spent at the comfortable Renoir home in the south of France and provided little indication of his outstanding talents, which were to turn him into one of the world's most honored and respected directors. Bertin's book, originally written in French, offers the colorful and meticulously researched portrait of a man passionately dedicated to the art of the cinema, though one wishes she had delved more deeply into his motivations and personal philosophy. Renoir was French to the core, and most of his outstandingly innovative work A Day in the Country,The Grand Illusion,La Marseillaise," and "Rules of the Game was created in France and not in Hollywood. Bertin does a carefully balanced, though occasionally a little pedantic, job in presenting Renoir the man and the artist - the French "exile" who, while in Hollywood, maintained a clear vision of the movie capital which, he wrote, "limits one's intellectual activity."