A nagging question that troubles many travelers about to take a vacation abroad is "Should I buy extra insurance?" Unfortunately, there's no easy answer.

Companies that provide various forms of travel insurance and protection can, of course, cite horror stories of what might happen if you don't.

Martin Weintz, vice president of WorldCare Travel Assistance Association of Washington, described the plight of an elderly Chicago man touring in Italy last year who suffered a heart attack. The cost to fly him home in an air ambulance was estimated at $60,000. Before the money could be raised, the man died.

John Noel, who heads Travel Guard of Stevens Point, Wisc., said his company has received more than 100 claims from customers in the Seattle region as a result of heavy December fogs that closed the airport temporarily. Many were headed for San Francisco and Los Angeles to board charter flights to Asia, and they failed to make their connections.

Under the terms of most charter tickets, a passenger who misses a flight for any reason can lose the full cost of the ticket -- amounting to hundreds of dollars for flights across the Pacific. However, those who had taken out Travel Guard's "trip cancellation and interruption" policy, said Noel, are being reimbursed for the cost of a one-way ticket on a scheduled airliner to catch up with their tour -- at least up to the limit of the coverage they had purchased.

In the rush of preparing for a trip, many people fail "to take a step back and evaluate their own protection," said Ray Greenly, a consumer affairs spokesman for the American Society of Travel Agents in Washington. "When something does happen, they regret that they didn't have insurance."

On the other hand, you don't want to buy insurance that you don't need, cautioned travel agent Philip Davidoff of Belair Travel Consultants in Bowie, who conducts professional training seminars for other travel agents across the country. He finds that most of his agency's customers who are going to standard tourist spots on a one- or two-week vacation trip already are adequately insured for medical problems or accidents that might occur while they are away.

It is important, however, to check what your regular policy does cover before you depart, a warning printed in U.S. passports. For example, Medicare does not cover health-care costs incurred outside the United States. If you rely solely on Medicare for health and accident protection, then some form of additional coverage is advisable when you go abroad.

Travelers also may already be sufficiently covered by their home-owner's or renter's policy for loss of luggage or valuables. Again, it is wise to check the provisions of your policy, especially if you expect to take along expensive photography equipment and valuable jewelry. "The best protection," said Davidoff, "is a good homeowner's policy."

Davidoff advised against buying extra flight insurance, which he said is "throwing money away," if you are properly insured for accidental death or injury that might occur on the commute home. His agency, as do many others, gives $100,000 in flight coverage free to customers at a cost to the firm of about 11 cents. Some travel-card companies, including American Express, also provide free flight insurance if you charge your ticket on their card.

Davidoff also suggested that travelers worried about losing the price of a ticket because of an airline suddenly going out of business should charge their ticket on a credit card rather than pay for default protection. There is no guarantee of a charge refund but you have a case for "going back to the credit card company and saying the service was not provided."

Travel insurance generally is sold through travel agencies, and agents can advise you on what they think you need. Ultimately, however, the decision is an individual one that depends a lot on your medical history and your destination. If your health is unstable or you are going to remote regions off the beaten tourist path, then you may want to consider additional protection seriously.

Even if extra insurance is not absolutely necessary in your situation, you may feel more comfortable having access to the supplementary services provided by some programs -- such as a 24-hour hotline for advice and help if you are injured or become ill. The peace of mind may be worth the additional expense.

Travel insurance -- or "assistance," as certain varieties are being called -- can be lumped into two broad categories. Gary Stone, professor of insurance at Michigan State in Lansing, defines them as protection against "property losses" and protection against "life and health risks." You can buy policies that cover one or the other or both.

Here is a look at what's available on the market today:

*Property protection: Usually the property you most want to protect is the cost of any travel arrangements, including deposits, that might not be refunded should you cancel a planned trip at the last minute. You may also want to insure your deposit against the possibility that the tour operator or airline suddenly goes out of business. This protection is offered by "trip cancellation and interruption" policies.

Such coverage is particularly advisable if you are buying a ticket for a charter flight. Federal regulations require the charter company to offer passengers cancellation insurance because of the severe monetary penalty -- as much as the full cost of the ticket -- if you miss the plane or sudden illness keeps you from going.

Depending on the policy, you can recover travel costs if you become ill and can't go or if illness or death strikes a family member, your traveling companion or a business partner. If, after the trip begins, you must return home suddenly for one of these reasons, the policy may pay for the cost of a one-way coach ticket. Bad weather, such as the Seattle fog, or other unforeseen circumstances -- including even a traffic jam that keeps you from catching a charter -- may qualify you for a refund.

How much you can claim is based on how much coverage you take out. Prices vary, but an approximate figure is about $5.50 for every $100 of coverage you want. This means if you want to protect against the possibility of missing your $500 round-trip charter flight to Europe, it will cost you five times $5.50 or $27.50. If a one-way standard coach fare home is $600, you might want to pay $5.50 more for the additional $100 in coverage.

Advance-purchase (APEX) tickets on scheduled airlines generally carry a penalty if you cancel within 21 days of departure. TWA, for example, imposes a $75 penalty or 10 percent of the ticket cost, whichever is higher, on flights from Washington to Paris -- a potential loss that could be avoided by taking out insurance. However, scheduled airlines tend to be more lenient about refunds if the passenger is facing a genuine emergency.

Before you buy a trip cancellation policy -- or any travel insurance -- make sure you know how much coverage you are buying and what is excluded, warned ASTA's Greenly. "I hate to read through the fine print of an insurance policy as much as anybody, but the exclusions are as important as what is provided."

For example, you may not be able to collect for an illness if you have a history of the problem. Also, some policies may pay if a tour operator or airline goes bankrupt but not if it defaults, a legal distinction that could leave you stranded abroad in either case. And you probably won't collect if a terrorist incident abroad convinces you to cancel a tour and stay home.

Both Travel Guard and the Travelers Insurance Companies of Hartford, Conn., two of the major travel insurance companies, offer trip cancellation and interruption policies that also contain lost baggage and some medical coverage. They are available through travel agents.

Under Travel Guard's "basic" plan, an individual traveler would pay $52 a week for $600 in trip cancellation coverage; $5,000 for emergency assistance, which might include medical evacuation home; $2,500 for medical expenses; $100 for baggage loss and $25,000 in case of accidental death. Additional trip cancellation insurance can be purchased at a rate of $5.50 per $100. For more information: Travel Guard, 1100 Center Point Dr., Stevens Point, Wisc. 54481, (800) 826-1310. Or consult a travel agent.

*Life and health risks: In recent years, a number of companies have emerged that promise what they call "assistance" rather than insurance for the traveler going abroad. At least three of them, including WorldCare, are based in Washington.

For a fee, determined usually on the number of days you will be traveling, the companies provide a variety of emergency services in case of sudden illness, an accident or death.

One of the major services is a 24-hour hotline, which you can contact for emergency help such as finding an English-speaking doctor or dentist.

Another is providing immediate funds for hospitalization. Foreign hospitals frequently require full payment for treatment before you are discharged, but you usually won't be reimbursed by your regular health plan until you return home. (The State Department through U.S. embassies can help arrange for an emergency transfer of money from relatives or friends at home.)

The third important benefit is medical evacuation home should it be required as the result of illness or injury. Some plans provided unlimited coverage; others set a specified amount. Evacuation can range in cost from several thousand dollars -- for a stretcher laid across several seats on an airplane -- to 10s of thousands of dollars for a private air ambulance and a medical staff to accompany it.

Judith A. Battaglia of Travel Assistance International of Washington said at this time of the year her 23-year-old company is busy arranging special transportation for American skiers injured in the Alps. If they have rented a car, for example, they may not be able to drive it back to the airport with a cast on their leg or hip. The company may, instead, take the skier to the plane in a van and take responsibility for returning the rental car. And, "We'll carry the luggage."

In addition to these specific provisions, assistance companies can provide a knowledgeable and experienced staff who will step in to help resolve any medical crisis you experience abroad, according to WorldCare's Weintz. "You are relieved of the immediate financial and administrative details encountered in emergency situations abroad."

For example, said Weintz, should you suffer severe burns in a traffic accident in North Africa, his firm could arrange -- through its network of doctors and hospitals abroad -- to fly you immediately to a treatment center in Europe prior to bringing you home, by air ambulance if necessary. It also has an on-call roster of doctors in the United States who can consult with foreign medical authorities.

WorldCare, which has branches in London, Hong Kong and Mexico City, also promises legal aid if you are arrested as the result of a traffic accident.

As an example of what assistance companies are offering, the WorldCare plan provides $7,500 for medical expenses; unlimited coverage for medical evacuation; round-trip air fare and up to $1,000 in living expenses for a family member to visit if you are hospitalized for more than 10 days; a one-way fare home for any minors who are accompanying you and might otherwise be left unattended; up to $1,000 in lawyer fees and $5,000 for bail; and -- if worse comes to worst -- shipment home of your body (which might otherwise cost several thousand dollars).

The plan excludes individuals who have had major hospitalization within six months or who are traveling against a doctor's recommendation.

The cost of the plan is $33 per person for travel from one to eight days; $39, up to 16 days; $46, up to 24 days; and $55, up to 32 days. An annual "membership" with unlimited trips up to 90 days each is $100 for an individual; $150, for couples; and $200, for families. Students or teachers taking a semester at a foreign school can enroll for six months for $170.

Among the assistance companies:

*WorldCare Travel Assistance Association, 2000 Pennsylvania Ave. NW, Suite 7600, Washington, D.C. 20006, (202) 293-0335 or (800) 521-4822.

*Travel Assistance International (Europ Assistance Worldwide Services), 1333 F St. NW, Suite 300, Washington, D.C. 20004, (202) 466-2919 or (800) 821-2828.

*HealthCare Abroad, 923 Investment Building, 1511 K St. NW, Washington, D.C. 20005, (703) 790-5655 or (800) 336-3310.