REMEMBER GREEN stamps? Remember what people used to do to get green stamps? Well, now that the airlines are giving their version, most notably in the form of "bonus miles" (which accrue and eventually reward free trips to frequent flyers), people are doing amazing things to get them.

Take, for instance, Irene (who, like everyone interviewed for this story, requested anonymity in the interests of respectability). Irene is married to a far-traveling tax lawyer and, according to her sister-in-law, "drives my brother like a teamster" in pursuit of free trips to Europe, which beats wholesale anytime.

Indeed, when Irene was approached on how she gets more for her--and her husband's--travel dollar, she announced, with a gay laugh, that it was good luck finding her at home as she had expected to be spending the day flying from New York to Omaha and back.

After which, for a mere $208, she would have achieved 10,000 miles on 10 domestic flight segments in a TWA special "Make-the-Most-of-Your-Mileage" contest running from Feb. 1 to March 31, thereby winning another free APEX round trip to Europe.

Her plan had been, says Irene, "to get up at 6 to be at the airport for a 7 o'clock flight to Omaha, where I would have spent 40 minutes for lunch and then gotten back to New York at 5:15.

"You see, I only had 9,900 miles and needed another 100, but I chose Omaha because it was the farthest I could go for the cheapest amount and also fly through St. Louis, so I could pick up the extra bonus of a thousand miles given for going in and out of there each way, all to apply to the regular mileage accrual for the 60,000 miles that wins two round trips to Europe or the Middle East.

"Right now my husband has got 3 1/2 round trips, with 30,000 miles to go for the next pair; I've gotten three round trips with a thousand miles to go to the next pair, so between us we have 6 1/2 round trips to Europe, and as we had planned to take the children to Europe anyway, it's all worked out very nicely."

She didn't have to go to Omaha after all "because I found out there's a 100-mile buffer and 9,900 miles was enough, so I went to the movies instead."

Although she keeps copies of routes and timetables, Irene claims not to go inordinately out of her way in scheduling trips. "The worst thing I did was book us to Portland via Los Angeles instead of direct when TWA had a double-mileage bonus on the flight to Los Angeles. I didn't know it was another 2 1/2-hour flight to Portland and my husband certainly didn't until we got on the plane and he looked at the map and then at me and said, 'Do you know what you have just done to us?' "

What really requires time and attention, says Irene, "is sorting out the mistakes the airlines make in posting the mileage--they give you stickers for the tickets and then somehow manage to lose a number of these tickets, and I once spent an hour on the phone and then all they managed to do was deduct 1,300 miles instead of adding seven segments."

(On Pan Am, which is offering the jackpot prize of a pair of first-class passes for a month's worth of unlimited travel when 175,000 miles are rung up, pilots not only announce flight time and weather but now also throw in the exact mileage.)

Airline employees are not always enthusiasts of bonus miles. Susan, who flies 125,000 miles a year as a middle management planner for an oil colossus, tells of a recalcitrant ticket agent in Cleveland who was not initially of a mind to give her credit for two segments on a direct flight to Denver.

Susan's original flight plan was a peregrination taking her from New York to Cleveland to Chicago to Denver to San Francisco (and back again the same way) "because that gets you 5,000 miles and on that particular junket they were giving a 25-percent bonus going from Cleveland to Chicago, counting toward the special prize for that period of the year, a free APEX trip to Europe.

"But the flight out of New York was delayed four hours, so I missed the connection in Cleveland and they wanted to boot me straight to Denver, so that I'd miss out stopping in Chicago, and they look at you like you're crazy--or worse--when you try to explain that you really do want to stop in Chicago, on your way to Denver, on your way to San Francisco.

"It was only when they promised that they would count it as two segments that I would get on the plane."

Such are the commotions of these new promotions, reports Vince, a record company vice president who covers the globe developing rock and roll acts, that airline personnel are starting to respond as though they've been turned into Stepford Wives.

"Since all these special deals have been offered, which practically required a Ph.D. in linguistics to figure out, there's all these yelling customers, particularly when the plane gets oversold--I'm not the only person doing this--and from the ground crews you're getting a lot of 'We will. Take care. Of you. In a moment.' "

Restraint, from the customer's standpoint, is acquiring bonus miles in what Vince refers to as "the course of life."

"I had already planned a business trip to the coast and a skiing vacation in Colorado, so it was just a matter of coordinating it when United sent me a voucher saying that if I took six legs that totaled 8,000 miles between like Feb. 1 and April 1, I'd get a free trip to anywhere they fly.

"So instead of flying direct, I changed planes in Chicago going out, for two legs instead of one, and then on the way back I changed to United from Pan Am--on which I was originally booked and which I'm also playing--to Salt Lake and changed planes for New York, and that was three and four. The skiing trip was five and six and I got it, a real easy bonus considering that it's usually real big numbers, up to the 70,000-mile range, to get a free round-trip ticket.

But even easier, says Vince, "was a letter I just got from Pan Am saying, 'Congratulations, here's your bonus ticket to the Caribbean,' and I don't know where the damn thing came from, I didn't even want to go to the Caribbean. It's like winning the lottery."

On reflection, he changes his mind. "It's like 'Let's Make a Deal.' Behind this door you get a free trip to Hawaii. And behind this door you get a free first-class trip to Hawaii. And behind this next door you get a free trip to Bora Bora.

"And every airline has a different deal."

Steve, who is in manufacturing and real estate in San Francisco, sums up: "I used to fly on whatever airline had convenient flights, but I will now be inconvenienced."

Nor does he shrink from inconveniencing his friends, one of whom, flying from San Francisco to Paris, was persuaded to change airlines and fly to New York under Steve's name so that the boarding pass could go back to Steve. (The friend, living in France, wasn't himself interested.)

As Steve sees it, "This is the first thing that's ever rewarded the business traveler who usually pays a higher fare because he can't take advantage of excursion rates."

Rewards thus far bestowed on Steve and his wife include vacations in Hawaii and Florida and a TWA roll to Milan to Rome to Cairo to Israel to Paris "and because we live in San Francisco it's always the longest flight, so we really get more for our buck."

For some, like Susan, it's the winning rather than the prize that spurred her to accumulate seven tickets on United, two on Eastern and one on TWA. Despite the effort to win, she hasn't had the time or even much inclination to use them.

"I used two on a trip to Hawaii with a boyfriend, but only because they had to be used up." As for the other five, she sighs, "One I gave to a friend, two are for my parents--I'm working on getting their hotel free through coupons collected from car rentals--and two I'm going to use for Hong Kong, to go to China."

She mainly plays bonus miles, says Susan, "because you get hooked on it, believe me."

She says there is not much discussion around the water coolers about who is getting what "because companies really frown on the whole thing and when your boss asks you why you always fly with stops, you say to save the company money."

Companies can't do much about it, says Steve, "because it would be too difficult for them to track what you're getting and besides you could have one airline issue a ticket and then exchange it for another and who'd know?"

Says a bemused TWA public relations man: "I swear I don't know how they get some of these things by their comptrollers. I just happened to be working on the computer the other day when my attention was caught by someone going from Miami to New Orleans via New York and somebody else going from Seattle to Los Angeles via St. Louis.

"Now, God bless these people, we like to think they're doing it because they just can't get enough of TWA's fine service, but are they saying that's the only way they could do it because everything else was full, or do they own the companies?"

For some weary travelers, it's enough of a prize to be upgraded into first class, a bonus being offered by most airlines to those who get into the 10,000-mile range, and for those who wouldn't dream of flying a mile more than they had to, free or not, bonus ticket brokering concerns are now springing up.

San Francisco's U.S. Coupon Exchange, which advertises in the Wall Street Journal, would, for example, buy a United certificate entitling the bearer to a first-class trip to any three cities in the United States for anywhere from $200 to $450 and then sell it for $650; but, says the proprietor of the business, he doesn't want to "chat about it" and besides, at 8:45 in the morning, he has four calls waiting.