It comes as something of a surprise, when you sit down and begin making a list, how many ways you can see a foreign country. This is especially true for western Europe, and particularly for Great Britain.

In decades past, travelers crossed the Atlantic for what essentially was an industrious round of sightseeing, taking in Buckingham Palace and the Eiffel Tower and Europe's other famous landmarks. These were the places the guidebooks said to see, and Americans on the Grand Tour or toting backpacks stood in line to visit them one after another.

But by now, many Americans have been to Europe several times, and some go every year. And grand as the Eiffel Tower is, you really don't have to climb it on every trip.

So what keeps the repeat visitors returning to Europe? Certainly the wealth of its history and culture remains a major lure, but there's another aspect. To meet the seasoned traveler's demand for something new, Europe increasingly has been packaged in unusual and interesting ways.

National tourism offices and private travel firms in the United States and abroad have created an inviting array of specialty offers, catering to the particular interests of frequent travelers. They range from gourmet feasts to archeological digs, to strenuous mountain treks and luxurious nights in castles and palaces.

And perhaps no place has been so thoroughly packaged as Great Britain, the most popular transatlantic destination for Americans. The British make it very convenient to see their cities and villages.

At the moment, Britain is one of this season's best travel buys. Air fares to London are an exceptional bargain: for example, $338 round trip from Baltimore/Washington International, daily through March 31 on World Airways, the lowest of the winter fares. Shopping bargains abound, too, because of the current strength of the dollar against the British pound, hitting record lows on the world's currency markets.

Here's a sampling of offbeat ways to see Great Britain, each choice providing, perhaps, a fresh look at familiar places:

* Castle Nights: Spend one night or several as "the guests of a family" in a private country manor or castle living the life of "the landed gentry." Since everything is prepaid (no money exchanges hands), you can pretend you are a pampered guest, eating breakfast and dinner with your hosts.

Many such homes have private swimming pools, tennis courts and stables for use by guests, and hosts can provide local sightseeing information.

Among the stately homes available is a 2,000-acre estate in Yorkshire in Northeast England, owned by the same family since 1723. Nearby is Castle Howard, featured in the "Brideshead Revisited" TV series.

The price varies greatly, but British Airways and Abercrombie & Kent International of Oak Brook, Ill., advertise a 12-day package to a series of such homes at $1,800 to $2,400 per person, including lodging, two meals daily, drinks and wine at dinner and a rental car.

For information: Abercrombie & Kent International Inc., 1000 Oak Brook Rd., Oak Brook, Ill. 60521, (800) 323-7308.

* Farm Holidays: This can be an excellent (and inexpensive) way to see Britain for a family with young children. A stay at a farm provides romping room for the youngsters; and since guest farms are scattered throughout Great Britain, they can be used as bases for touring.

You can find a working farm alongside a good fishing river, in a pony-trekking center for the children or near a quaint village out of the past. Join in the work or visit with the hosts at mealtime.

The British Tourist Authority publishes a booklet listing dozens of individual farms and several agencies that handle bookings for farm holidays. The prices range greatly, depending on the quality of accommodations, the number of guests and meals included, but farms tend to be much cheaper than hotels.

For information: British Tourist Authority, 40 West 57th St., New York City, N.Y. 10019, (212) 581-4700.

* Drive Yourself Bed-and-Breakfast Tours: Britain is famous for bed-and-breakfast lodging, small establishments offering basic accommodations (and breakfast) for a small price. Even in the busy summer season, say British travel officials, you can usually find a place to stay.

One of their charms is that they make it easy to explore the countryside without making advance reservations. But if security is what you want, that is available, too. The British Tourist Authority (see item above for address) distributes a brochure listing B & B reservation services, which will book one night or your entire visit.

An alternative is "Britain on a Budget," a B & B voucher program, offered by a Portland, Ore., travel firm, that combines an unplanned itinerary with the security of guaranteed prices. This is how it works:

Travelers purchase vouchers for six nights in England, Scotland or Wales, good for use at more than 300 "selected" farms and country houses. A confirmed reservation is made for the first night's lodging, but participants phone ahead daily for subsequent nights.

The 1985 price for two people is $450, which includes six nights' lodging, six full English breakfasts, a compact rental car with unlimited mileage for seven days and various taxes.

For information: P.T. International, 1318 Southwest Troy St., Portland, Ore. 97219, (800) 547-1463.

* Handicraft Weeks: Here is a chance to learn a craft or improve your talents under the week-long guidance of a British craftsworker, while sharing his or her home, meals and studio.

The Association of British Craftsmen offers crafts vacations year-round in a variety of arts, including ceramics, pottery, glass-painting, weaving, silversmithing, making musical instruments, cabinet-making, calligraphy, furniture restoration and leatherwork -- for beginners as well as experts.

The cost varies, but figure on about $250 a week per person (double occupancy) for room, meals and instruction.

For information: Avocations (Bristol Crafts) Ltd., 57 Coombe Bridge Ave., Stoke Bishop, Bristol, Avon BS9 2LT, England.

* Walking Tours: Hiking outfitters offer walks through practically every part of England, Scotland and Wales, including inn-to-inn and camping excursions, guided or do-it-yourself. The British Tourist Authority in New York maintains a list of outfitters.

Among the trips available is "The Lake District," a five-day guided walk through the lake region of northwestern England, staying in country inns and hotels. A van shuttles the luggage, so you only carry a day pack.

This is a land, says the tour organizer, "of grand castles and quaint villages, sheer cliffs and quiet valleys, mountain screes and grassy moors."

Departures April 26 and July 26, costing about $75 a day per person for land arrangements.

For information: Sobek Expeditions, Angels Camp, Calif. 95222, (209) 736-4524.

* Bicycling Tours: Trace the back roads of Britain on a bicycle. "Scotscycle" is a two-week, 10-speed guided tour of Scotland's "castles, coasts and misty hills," with a choice of nightly accommodations in hotels or bed-and-breakfast inns.

The pace is easy, promises the outfitter, with plenty of time set aside for hikes, museum visits, leisurely lunches at wayside inns and naps on the beach. The cost is $1,545 per person (double occupancy) in hotels and $1,020 in B & Bs. Departures June 8 and 22; July 6 and 20; and Aug. 3, 17 and 21.

For information: Sobek Expeditions, Angels Camp, Calif. 95222, (209) 736-4524.

* Garden Tours: England is a land of gardens and gardeners, some of whom became quite famous in other pursuits. "English Literary Landscapes," a two-week tour, attempts to "weave together writer, place and landscape" in three areas of Britain -- Sussex/Kent, Cotswolds/Bath and Yorkshire. It is offered by Serendipity Garden Tours of Cambridge, Mass.

Departure is May 30, and the trip will be led by Mary Nash, a teacher of creative writing at Radcliffe College, and Stella Palmer, an English garden historian.

The motorcoach itinerary includes visits to the village of Rye, where Henry James lived; the forest of A.A. Milne, and the homes and gardens of Jane Austen, Rudyard Kipling, Lewis Carroll, Winston Churchill, Virginia Woolf and the Bronte sisters, among many others.

The cost is $3,400 per person (double occupancy) and includes air fare, lodging, breakfasts and dinners.

For information: Serendipity Garden Tours Inc., 3 Channing Circle, Cambridge, Mass. 02138, (617) 354-1879.

* History Tours: So much of the attraction of Great Britain is its historical heritage. "The Royal Stuarts," a 17-day motorcoach tour of "the notable places of intrigue and battle" associated with the House of Stuart in Scotland and England, is offered by the History Book Club of Stamford, Conn.

Departing May 2, it will be led by British historian Ronald Hutton, lecturer on Stuart history at the University of Bristol. Four days in Edinburgh, at the tour's outset, focus on Mary, Queen of Scots. The cost is $2,695 per person (double occupancy), including air fare, lodging, breakfasts and nine dinners.

For information: Great Journeys Ltd., 80 State St., Newburyport, Mass. 01950, (800) 225-2553.

* Canal Cruises: Explore the British countryside by water, cruising the numerous inland waterways in the English Midlands built during the Industrial Revolution. One route takes you through Stratford-upon-Avon, Shakespeare country.

You can rent a "skipper-yourself" boat for a week, something of a floating home, which is reasonably easy to manage, even with no prior experience. Or rent a boat for your group (two to 12 persons) with a captain. Or you can take a cruise aboard a canal barge, a "floating hotel," where the captain and crew do the work.

For more information: The U.S. representative of UK Waterway Holidays Ltd. is Dial Travel, 311 North Charles St., Baltimore, Md. 21201, (800) 424-9822.

These examples are only a sample of the wide variety of travel opportunities offered in Great Britain and, similarly, in much of the rest of western Europe.

It often takes a little homework to uncover unusual trips. A place to begin is the national tourist office of the country you plan to visit. Most are represented in New York City.

Be specific in any request: Ask for information on "walking tours," for example, or "walking tours in the Lake District."