Forgive and forget. That's the motto your local public libraries (and some college and university libraries) are adopting this week. If you're willing to haul in all those overdue books, librarians are willing to overlook the fines. It's all in the spirit of National Library Week, a time to realize that your library card is the cheapest charge card you own. And probably the only credit card that won't be lowering your credit limit. Consider these benefits that are yours for the flash of a card at your local libraries:

Never get caught saying that the library's too far away. It can't be. Anyone living in the Washington area can borrow a book from any local public library (except Alexandria and Arlington). Just drop in and pick up a card. Most lbraries also offer bookmobiles as well as delivery service for people unable to leave home because of handicaps or illness.

Let your fingers do the walking. You don't even need a card for this. Pick up the phone and call any library reference desk. Ask them something perplexing, such as whether a certain word is legal in Scrabble or the out-of-town address of a company you want to write to -- you name it, the wizards at the reference desk have heard it all. And they know where to find the answers.

If you're brushing up on local history, remember that every library system has its own special collection of documents, books and photographs that trace your region's roots. Prince Georges County also boasts a collection of books and magazines on horses.

Entertaining tonight, but the walls are bare? Charge out a framed reproduction of a masterpiece (available at many libraries). Fairfax County even has circulating sculptures and puppets. m

Many smart library patrons have organized their own exchange of sewing patterns, which anyone can borrow if they leave one of their own in return. The same goes for coupons.

People with vision impairment should remember that many libraries lend talking books, magnifiers, large-print and braille books.

Looking for a place for your club's meeting? Arrange to use your library's meeting room.

Got a health question? Call the Prince Georges County library's TEL-MED line, which offers tape-recorded messages on more than 200 medical subjects. Dial 345-4080 and ask for tape number 429 for details.

Tired of re-runs? Borrow an Academy-Award-winning film and throw a movie-party.

Struggling artists, collectors and craftspeople, take note: You can get free exposure in the display cases of most area libraries.

When the kids find that the novelty of dialing the weather and time voices has worn off, tell them about the D.C. library's Dial-A-Story (638-5717), a taped fairy tale which runs continuously and changes weekly.

These are just inklings of the new personality that libraries are assuming these days as book-lenders, advice-givers and entertainers all rolled in one. Call one of your libraries for a free brochure of activities and services.