ASK ANY TRAVELER about the most persistent fears and trepidations that arise when headed away from home, and high on the list will be one that surfaces on many trips.

Will my baggage arrive, in one piece, when I do -- or, if not, will it show up at all?

Who among us has not heard at least one horror story of manhandled suitcases, misrouted bags, mysterious thefts of cameras, or having to begin a vacation at a posh beach resort with little more than a toilet kit because luggage containing a week's wardrobe had disappeared? Though most bags arrive on schedule, as a rule, there are always unfortunate exceptions.

Since there are no quick, easy or new ways to keep these problems from developing, wise and wary journeyers always assume the worst will happen and then take steps to cut possible losses. They do not pack jewelry, money, cameras or similar valuables--they carry them. And they figure that the only guarantee against mishap is to be prepared--to collect from an insurance company.

Some insurance is provided automatically with the passage. Domestic airlines will now pay up to $1,000 total per ticketed passenger for lost or damaged luggage--regardless of how many pieces are checked. Certain items are not covered, so it's important to query each airline being flown. The liability of foreign airlines may vary and can be considerably less than what U.S. lines accept; both Air France and British Airways, for example, pay only $20 per kilo (2.2 pounds). Travel agents may not be able to quote liabilities without phoning the carriers being booked, and some have never been asked the question by a client.

Amtrak pays up to $500 per ticketed passenger ($2,500 maximum under the family plan). Individual cruise lines set different limits; Cunard offers a maximum payment of $100 per passenger, Norwegian Caribbean $300 per passenger. Both Greyhound Bus Lines and Trailways pay a maximum of $250 per adult interstate ticket. You can, of course, buy additional baggage insurance, sometimes from the carriers (if purchased from airlines, the cost usually ranges around 50 cents per $100 of value). And some homeowners' policies provide coverage. Naturally, in all cases it's necessary to provide satisfactory proof of loss.

Now comes enterprising, ubiquitous American Express with the announcement--perhaps soon to be duplicated by other charge card issuers--of free baggage insurance for its card holders.

All "U.S. cardmembers are automatically insured against loss of or damage to their baggage" anywhere in the world when they charge their plane, train, ship or bus tickets on the American Express Card. The new insurance, up to $1,200 per trip, includes both checked and carry-on items for each member, spouse and dependent children under 23 if their tickets are also charged on the card.

Some personal items such as cameras, briefcases and sports equipment are covered, and baggage is also insured while traveling in licensed public limousines, taxis or airport buses to and from an airport, terminal or port of embarkation--even within the terminal building--if tickets were purchased before the trip. Reimbursement will be for "replacement cost today, less depreciation," a spokesman explained.

FOILING BURGLARS: Both domestic and foreign airlines now require that all checked baggage have some type of external identification to facilitate its return if misrouted or if the destination tags get torn off, and to reduce the chances of look-alike suitcases being picked up by the wrong passsengers.

Many experienced travelers never put their home addresses on luggage, usually substituting their business addresses, or even just their name and a personal number, to avoid alerting thieves who may be scouting the terminal to find out what homes may be left temporarily unoccupied. A clever burglar could conceivably get a tip on a prospective victim merely by looking up a name in a phone book or city directory. The complete home address should, carriers insist, always be attached inside the bag.

Joseph Travis, president and chairman of the board of Near Inc., has serious doubts about current airline practices. Near is an Oklahoma firm which specializes in emergency medical evacuation by air of members who become seriously ill while traveling overseas. Members of the International Air Transport Association are authorized to permit passengers to use only their initials and a passport or other number, but U.S. airlines have agreed to require that outside labels carry ticket holders' names. Travis notes that the blank labels supplied by airlines ask for complete addresses; thus passengers may be directly or indirectly influenced by airline ticket agents to affix their home addresses, he says.

A spokesman for the Air Transport Association of America, which represents 30 major domestic lines, says no law enforcement agency has "ever brought to our attention" any cases in which a name on a luggage tag facilitated a burglary. "There are so many easier ways" for a thief to discover unguarded homes, he adds.

Travis has urged the airlines to adopt a "safer system" by adding to passenger information already in their computers the baggage tag numbers assigned each passenger with luggage at check-in. This would eliminate the need for any outside labels, Travis says. Using passport numbers, he points out, does not facilitate prompt return of missing baggage. Airline and other industry officials have replied that they are satisfied with the present system.

Meanwhile, Travis is offering travelers free baggage tags (one per person--10 million tags have been prepared) marked with an identification number and Near's toll-free phone number. (Some organizations have provided such a service in the past, for a fee.) If a bag is lost, and the finder reports the number to Near, the firm will look up the owner's name and address on file and arrange for the bag's return. This is an extension of a system already available to members of Near, which also offers others travel services.

For a tag or further information, write Near Inc., 1900 N. MacArthur Blvd., Oklahoma City, Okla. 73127, or phone 1-800-654-6700.

Another way for cautious travelers in the Washington area to foil burglars, suggests Louis W. Moses, president of 1st Federal Safe Deposit Co., 4801 Massachusetts Ave. NW., is to use his "short-term safe storage plan."

The firm provides a special container large enough to hold a silver service, tea service and candlesticks "as well as various other business or personal items" but no breakables. After the customer packs and locks the box, it is picked up by an unmarked vehicle operated by bonded and insured staff members, who drive it inside the building and deposit the box in the vault. When the traveler returns from the trip, the valuables are delivered.

CUSTOMS RAISES EXEMPTIONS: Some tourists are much more interested in what they can bring back from a trip out of the country than in what they take with them. The good news from U.S. Customs is that shoppers are now permitted to pack more duty-free items in those suitcases.

Each returning U.S. resident can now claim a $400 exemption (raised from $300). If you're coming home from the U.S. Virgin Islands, American Samoa or Guam, you are entitled to an $800 exemption (previously $600), provided that not more than $400 of the purchases were acquired outside those insular possessions.

In addition, a U.S. resident who exceeds the exemption will pay only a 10 percent flat duty rate on the next $1,000 worth of goods (the rate drops to 5 percent if those goods were acquired in one of the insular possessions).