Bargain-hunting travelers have made frequent-flyer programs one of the airlines' most successful promotional ploys in recent years, and the prizes keep getting bigger and better.

The name of the game varies from carrier to carrier, but its purpose remains the same: to entice customers from competitors and build consumer loyalty by giving away prizes. Any passenger can play -- and millions do.

The idea is that passengers are given mileage credits based on the number of miles flown and on the number of trip segments completed in various classes, according to the rules of the particular airline. Extra miles also may be awarded. Mileage totals are regularly updated in the airlines' computers.

Prizes vary from program to program, but specific totals of miles in the thousands can qualify passengers for upgrades (such as from coach to first class -- without charge or at a discount), free flights in this country and abroad, free accommodations around the world, free rental cars or upgrades and free cruises.

A number of U.S. carriers also have agreements with each other, various foreign airlines, hotel chains and rental-car companies, under which frequent flyers can earn additional mileage credits by flying those partner carriers and patronizing participating hotels and rental-car firms.

Among major prizes currently offered: A free 10-day Holland America cruise/tour to Alaska for two plus two free connecting round trips, any class, on United Airlines -- for 300,000 miles in United's "Mileage Plus" program. Two free first-class round-trip tickets on Pan Am between North America and selected destinations in Africa, South America and Asia, including free coach travel on American Airlines (as available) to and from the North American gateway city, seven consecutive days free rental of a full-size car and 35 percent off the room rate at certain participating hotels -- for 175,000 miles with American's "AAdvantage Program." Two free first-class round-trip tickets on Continental Airlines to the Pacific, including one week's free rental of a full-size car on the U.S. mainland or in Hawaii and four free consecutive nights at any Marriott hotel or resort worldwide -- for 150,000 miles in Continental's "TravelBank."

Every major U.S. airline has a frequent-flyer program. Application forms can be picked up from any airline office; some lines give new members a few thousand free miles just to open their accounts. Membership is free except for Pan Am ($25), Continental ($25) and Air Canada ($20). But Air Canada says it often waives the one-time fee for U.S. members, and both Pan Am and Continental increase the number of free miles as an added incentive when you sign up. (The airlines say fees help defray administrative costs of the programs and also help discourage infrequent flyers whose accounts might remain inactive.)

American Airlines introduced the concept in 1981 with its "AAdvantage Program." Today you can choose from Pan Am's "WorldPass," TWA's "Frequent Flight Bonus," Delta's "Frequent Flyer Automated Mileage Program" and similar programs operated by other domestic carriers.

Some foreign carriers have plans that operate independently of U.S. carriers -- such as Air India's "Frequent Traveler Plan" and El Al's "Matmid." On a number of other foreign airlines, passengers can accrue mileage toward domestic airlines' programs when departures for overseas are made from certain U.S. gateway cities. For example, you can add mileage to your United "Mileage Plus" account by flying Air France, SAS, Lufthansa or Alitalia.

Although frequent-flyer bonuses have proven most valuable to those traveling on business -- the airlines' best clients -- even travelers who fly less frequently and primarily for pleasure can benefit. Often upgrades can be earned with only a few thousand miles.

Travelers are continuing to play the game and claim their awards despite frequent complaints that some lines have been slow to give proper mileage credit. According to various carriers, mileage is credited anywhere from three days to a few weeks after proper documentation is received from the member. One airline indicated that some complaints about long delays may have been caused by the line's lack of computerized records when its program was first started.

With most major U.S. carriers offering long lists of prizes worth hundreds of dollars, the Internal Revenue Service has been prompted to consider taxing the free flights and other awards as fringe benefits.

The IRS held public hearings last March as it sought comments from airlines, travel agents, employers and others about problems that might arise if frequent-flyer benefits were required to be reported and taxed. Major considerations include how such bonuses would be valued, whether they should be treated as wages subject to withholding and how the tax would be withheld.

Regulations are now being drafted, but an IRS spokesman said last week it was not possible to predict how long the process would take, nor what form those regulations might take. More public comments may be requested before final rules are issued, he said.

At the same time, some corporations have been formulating policies stating that any bonus awards to employes that result from business flights paid for by the firm should be considered the property of the employer. One corporate concern is that if some employes favor one carrier simply to acquire more points, the preference may cost the company more money.

For some frequent flyers the quickest, most direct flight is not always the ticket to the friendliest skies. Lured by the promise of bonuses, they sometimes select a more circuitous route with multiple stops and flight changes (more flight segments can mean extra points), even though there may be shorter, faster and perhaps cheaper routes to their destinations. Any inconvenience or extra charges, they reason, will be more than covered by the money they save on the free trips they earn.

In response to corporate interest, Japan Air Lines has three frequent-flyer programs designed for different memberships: "JAL Mileage Bank -- North America" (for individuals), "JAL Corporate Mileage Bank" (for both individuals and companies) and "JAL Corporate Passbook" (solely for companies).

Partner agreements between airlines generally allow members of one frequent-flyer program to accrue miles for that program's awards by flying on another carrier, but rarely can mileage be transferred between different programs. However, it is important that participants keep track of mergers between airlines, other continuing changes in the industry and the current connections between carriers. For example: Eastern announced recently that members of its "Frequent Traveler" program can earn mileage credits (for Eastern's programs) by flying Continental. And Continental's "TravelBank" members also can earn such credits for their own program by flying Eastern. (Continental's parent company, Texas Air Corp., recently agreed to buy Eastern, although final approval of the merger by the Department of Transportation is still pending.) But the two frequent-flyer programs are operated separately, with different awards and although passengers can belong to both, they must choose at flight time which program they wish the mileage credited to.defbox Texas Air owns New York Air, and the latter's frequent-flyer program recently was merged with Continental's "TravelBank." But at present, passengers who were members of New York Air's program are not allowed to earn "TravelBank" credits by flying Eastern. TWA members can use credits for JAL flights, as can passengers in Delta's program, but TWA and Delta have no reciprocal arrangements. Because United acquired Pan Am routes in the Pacific, the latter's flights to that area are among awards in United's program; but credits in the frequent-flyer programs of the two airlines are not exchangeable. Pan Am "WorldPass" mileage can be used to qualify for certain American Airlines' awards, but credits cannot be exchanged in reverse. It is also important to keep your own record of the flights you make and credits due you. While the airlines will mail a computerized statement of your mileage account -- usually every four to six weeks, if your account is active -- errors do occur. Check statements to see if the number of earned miles listed is correct.

And always hold on to the used ticket coupon and boarding passes (and hotel receipts or car-rental agreements). Passengers usually are identified before boarding by their computer number, by a special sticker they must affix to the ticket or some other method by which the mileage for the flight can be credited. But tickets sometimes go astray, stickers can fall off and computers may go awry. You will be required to produce proof of travel, as stipulated by the rules, if you need to ask for an adjustment in the airline's records.

Remember that some lines have blackout periods -- holidays, for example -- when free trips cannot be used; there also may be arrival/departure restrictions at hotels, and some bonus awards must be used before prescribed cutoff dates make them invalid.

In addition, airlines have rules concerning who may claim and use bonus awards besides the frequent-flyer club member who earned the mileage, and how mileage totals can be transferred. United Air Lines has been sued by one of its "Mileage Plus" members, who was ejected from the program last year -- after earning more than $100,000 in bonuses -- for sometimes permitting a family member to fly on his ticket and then having his account credited with the total mileage earned. United maintains that you can transfer your own mileage bonuses from your personal account to other members of your family, but the other way is not permitted. No trial date has been set.

Finally, what do frequent flyers do if they fly so much they're tired of taking trips but have piled up thousands of dollars in free flights? Many of them sell their airline bonuses at a discount to coupon brokerage firms like AGCO in Silver Spring, Md. AGCO adds a small markup for profit, then resells the tickets -- primarily first class in this case -- to eager bargain-hunters at prices well under current airline fares.

There are also airline rules that forbid selling or bartering these free tickets outside the family, but many lines do not check. Alan Gross, president of AGCO, says Pan Am coupons are the only ones brokers avoid because it is the only major airline whose rules flatly prohibit transfer of such awards to anyone other than the member who earns them and a companion.