Here's a rundown of what's new in paperback _ new versions of some of the old classics as well as some original books:

* Just in time for the elections, and for those who take their government seriously, is the re-release of Alexis de Tocqueville's "Democracy in America" (Harper & Row, 778 pp., $14.95). As relevant now as it was when it first hit the book shelves in 1848, the French writer makes astute observations on American life, politics and morals. The modern-day reader, however, may find equally entertaining de Tocqueville's errors, such as his view that the centralized government would continue to deteriorate in the face of stronger state governments, and that one day there would be no more Mexicans in the province of Texas.

* Puccini's popular opera "La Boheme" was taken from a novel written in 1851 by Henri Murger. Readers will see from the work, "La Boheme _ Scenes de la vie Boheme," published in translation (Peregrine Smith, 306 pp., $10.95), why Puccini and other composers were so taken with Murger's portrait of Bohemian life. There is a problem, however. Elizabeth Ward Hugus literally translated some of the French phrases and colloquialisms word for word, rather than seeking a smoother phrasing. This is a constant irritant to the reader trying to capture the flavor of Murger's words.

* Owen Wister's classic Western tale, "The Virginian," takes its place in Penguin's collection of classics in this new edition (454 pp., $4.95) with an introduction by John Seelye. The story of the stranger who came to the Wyoming territory inspired many a similar tale and later films, and the character became an prototype for the Western man. This edition includes explanatory notes and suggestions for further reading.

* Every Cliche in the Book, by Peggy Rosenthal and George Dardess, illus. by The CRAG and Peter LaVigna (Quill, 219 pp., $8.95) This is more than just a collection of cliches, it's a very funny grouping of cliches, used in dialogues and accompanied with truly rib-tickling illustrations. The authors give sources for some of the cliches and find a number of positive reasons for using them. It gives you a fresh look at our daily speech.

* In the late 1960s, almost an entire generation was swept into the world of J.R.R. Tolkien in "The Lord of the Rings" and his earlier work "The Hobbit." This is the 50th anniversary of the publication of "The Hobbit" and to mark that date, Tolkien's work is being reissued. For those too young, too old or too out of it to have followed the marvelous adventures of Frodo, Gandalf, Strider and Bilbo Baggins, Ballantine has published both "The Hobbit" and "The Lord of the Rings" in paperback ($3.95 each).

* E.M. Forster's "A Room with a View" (204 pp., $3.95) has been reissued as part of the Bantam Classics series. The story, which recently became an award-winning film, is a portrait of mores and manners and romance. Written in 1908, it rings as true now as at the turn of the century.

* Homework Without Tears, by Lee Canter and Lee Hausner (Perennial, 157 pp., $7.95) If your child is just starting school or is having trouble getting the homework done, this book will help you work with him or her to develop good habits. The authors give simple suggestions, check sheets and lists that will help you eliminate some of the problems and help your child learn to plan his or her work.

* With the difficulty of finding good and affordable day care centers, some parents might consider organizing their own play groups for pre-school children. Sheila Wolper, who runs a program in New York, and writer Beth Levine have written "Playgroups" (Pocket Books, 190 pp., $6.95), which describes what's involved in getting started, what qualifications are needed for personnel, getting organized and organizing activities for the children. A handy basic guide for anyone considering such a move.