(MONEY Magazine) – The sea is alive with myths and legends. The condemned Flying Dutchman. The accursed Ancient Mariner. Or the saga of Moby Dick, the great white whale. But to the modern ocean traveler the most horrifying specter of all is that of the Caribbean cruise ship, crammed stem to stern with medicated ancient mariners on pensions and their white-whale mates off on a carefree cruise to nowhere. Just the thought is enough to curdle your chowder. But the news is: it ain't necessarily true anymore. In the past five years, cruise vacationers ages 25 to 34 have grown from 13% of the total to 17%. Roughly a third of all cruisegoers are under 35. And only 23% are over 65. Nonetheless, 95% of Americans have never taken a cruise vacation, and the reinvigorated cruise industry wants to pipe them aboard. According to Arthur Frommer, travel expert and author of The New World of Travel, current bargain fares result from an overcapacity of cabin space created by the shipbuilding boom of the past decade. The current number of berths -- about 60,000 -- is more than twice the total 10 years ago. And more ships are a-building. The Cruise Line International Association reports that by 1990, 16 new ships will be added to the 103 now afloat. The new ships include Royal Caribbean Line's Sovereign of the Seas, the colossus that carries more passengers (2,690) than any other cruise ship in history. Clearly the lines are toiling to fill those new cabins by offering families and the affluent thirtysomething crowd tempting prices and a sophisticated array of on-board activities. ''It suits my life style just fine,'' says Californian Doris Hanley of the 12-day cruise she took to Alaska this summer on the Sitmar Fairsky with her two daughters and grandson. It cost $11,500 for the four of them and was Mrs. Hanley's second cruise this year. ''I don't have to pack and unpack. And we wouldn't be back if there weren't enough for my grandson to keep busy.'' While on-board counselors supervised the six-year-old in the ship's youth center, the adults' choices included visiting the onion domes of the old Russian city of Sitka or taking a helicopter excursion to tromp atop Mendenhall Glacier. In the evening they could watch first-run movies, hit the casino or catch live entertainment in the ship's six lounges. James Michener, author of the bestseller Alaska, came aboard in Ketchikan to talk shop with passengers. At dinner, one of the specialties of the ship is fresh salmon: after shore excursions, the Fairsky chef stands ready to cook the personal catch of anglers. And dessert, of course, was baked . . . well, you know. Cruising to Alaska is rapidly gaining popularity because of the dramatic vistas and the unusually calm passageway. But the most popular destination for the 3.5 million American cruise vacationers this year -- up from 500,000 in 1970 -- is still the Caribbean. Albert and L. Jean Young of Buffalo, N.Y. liked their experience on Royal Caribbean's Sovereign of the Seas. ''The ports of call are fabulous,'' says L. Jean, a police officer. The ship stopped at St. Thomas, Haiti and San Juan, where some passengers disembarked for golf. ''The exercise program is good,'' she notes, ''and the activities are endless.'' That's fortunate because, she adds, ''Our only complaint is that the rooms are on the small side.'' One reason these regal excursions are gaining in popularity is that prices are beginning to beat competing vacations. The best way to figure it is to break down your cost per day. A bargain seven-day cruise will cost you $175 a person. Moderately priced ones, like the two described above, will run $175 to $300. Above that is the deluxe level, found on ships such as Cunard's Sea Goddess I and II and starting at $450 a day. Note that a typical seven-day Caribbean cruise, which costs $1,000 to $1,500 a person, will include air fare to your ship from most major cities, all meals and all shipboard activities. Not bad when a good room alone in an island resort hotel can cost $200 a night or more. Ship passengers need cash, credit cards or traveler's checks only for shopping, bar bills and tips. * Your first port of call should be a travel agent. It's virtually impossible to book a cruise directly from the cruise company. If your agent is a member of the National Association of Cruise Only Agents or is certified by the Cruise Line International Association, he should be able to offer you better options and prices than you could find on your own. Indeed, agencies that are high-volume producers for some lines, such as Princess (which recently acquired Sitmar), Cunard and Royal Viking, are often able to provide clients with special amenities such as priority dining room seating and invitations to the captain's cocktail party. Ask your agent whether he belongs and whether he can find you a discount fare. ''On maybe half the cruises around, it's possible to pay less than the brochure price,'' says Josephine Kling of cruise specialists Landry-Kling in Miami. Here's how: -- Book far in advance. This is the easiest way to save money. By paying three to six months pre-departure, you can save several hundred dollars. Royal Caribbean cruises, for example, are as much as 20% lower if you plan that long ahead. -- Or book at the last minute. A few lines offer cut-rate fares to fill last- minute vacancies. If you book on the Seaward, a new Norwegian-Caribbean Line ship, within 30 days of embarkation, you can pick up a choice outside stateroom for only $749 a person on its seven-day western Caribbean cruises. Normal minimum fare is $1,295 for an inside cabin. -- Buy off-peak. That doesn't always mean the Caribbean in August, either. There is often a slack period right after New Year's Day when prices can fall by 10% to 20%. -- Go with a group. When you pick up the Sunday travel section of your newspaper and see a low price, it's because the agent has reserved a discount block of tickets. Don't worry, you won't have to face off every morning with a cruise leader armed with a clipboard and a whistle. Booking with a group does not necessarily mean that you travel in a group. -- Make your own arrangements to get to the boat. Since most North American cruises include air fare to the point of embarkation in their price, you can sometimes have the flight premium subtracted from your total tab and then get to the pier cheaper on your own steam. -- Singles should not despair. The industry standard is that single occupancy of a stateroom costs at least 150% of the per-fare for double occupancy, but on Princess the surcharge is only 125%. In off-peak periods, Royal Caribbean's guaranteed single-stateroom price is nearly the same as its double-occupancy rates. And if you are willing to share a room with a stranger (same sex only), cruise lines can often arrange a deal. -- Bring along the kids. Third and fourth passengers in a stateroom will usually be charged less than half the lowest stated adult rate. Most lines encourage youngsters and go out of their way to provide scavenger hunts, masquerade parties and video arcades for them. For adult cruisers there is plenty to do on a ship -- or nothing at all. Passengers who wish to just lie by the pool or play bridge can do so. Those interested in late-night discos or organized silly games can do that too. Each ship and each cruise has its own personality. The longer, more expensive voyages typically attract older passengers. Shorter trips -- those of a week or less -- attract a more active, more youthful clientele. Carnival Cruise Line, whose cruisers are called the Fun Ships, is probably the leader in this market, with some of its cruises getting positively Winter Carnivalish. List prices for a typical island-hopping, seven-day cruise range from $995 to $2,095. For a trip that feels less like a stay in a hotel and more like an encounter with the sea, try Windstar cruises in the Caribbean, Mediterranean and South Seas; these brand-new, computer-controlled four- masters carry 150 passengers and are powered alternately by wind and diesel. Typical fare: $2,895 for seven days. Food is one of the big selling points for cruises, so it's plentiful and exotic. On a Royal Viking cruise in Scandinavia, for example, expect the choice of roast reindeer one night. Ships stopping in American ports will be inspected by the Centers for Disease Control twice a year to prevent outbreaks of food poisonings such as the two instances of shipboard stomach upsets reported in 1986. It's a rigorous evaluation. ''If the same standards were applied to restaurants and hotels on the mainland, at least 80% would fail,'' says Douglas Ward, author of the Berlitz Complete Handbook to Cruising. Ships that don't pass will find themselves on a CDC list. For a free copy, write to the chief of the Vessel Sanitation Program, Center for Environmental Health and Injury Control, 1015 N. America Way, Room 107, Miami, Fla. 33132. On their first cruise, most Americans opt for the Caribbean or the Bahamas, where 83 ships sail, 30 of them year round. Cold weather is peak time for Caribbean cruises, of course, and summer is prime time for 23 ships traveling along the West Coast to Alaska and back.

Travelers eager to leave North America should investigate the more than 60 ships that sail off Scandinavia and in the Mediterranean. Or catch the original Love Boat, Princess Cruises' flagship Royal Princess, for a 12-day trip from Venice to Naples via the classic Mediterranean cruise ground among the Greek islands ($3,140 to $8,850). Finally, consider the ultimate luxury -- an around-the-world cruise. You can spend up to $91,180 next winter on a three-month globe-girdler on the luxurious Cunard Sagafjord. Or you can circle the globe on the Soviet liner M.S. Leonid Brezhnev, with stops in Bali, Cadiz and Curacao, among other ports of call on her 94-day itinerary. Unlike the Cunard package, you do have to pay air fare to the ship's home port in Southampton, England, but you can see the same world for a very uncapitalistic $83 a day.

BOX: Checklist Five salty tips

-- Request a cabin in the forward or middle part of the ship. Engine vibration is usually more noticeable at the stern. -- If you book an expensive upper-deck, outside cabin, ask if your view is unobstructed. Many upper-deck portholes look out on lifeboats or ventilators. -- If you are seasick-prone, ask your doctor to prescribe Transderm, an antinausea drug attached to a patch that you wear behind your ear. -- Men, do not be tuxedo intimidated. Except on the most elegant ships, such as the Sagafjord, perhaps 40% of the men will dress in conservative business suits on formal nights. -- Rules for tipping. Waiters and room stewards each get $3 a day. Add 15% to all bar tabs.