Travelers crisscross the globe with frequent-flier immortality at stake

In between these flights, Wallin, who has a sales job in Stockholm, says he will only occasionally step foot outside an airport. The goal of all this marathon flying: one million frequent-flier points.

Scandinavian Airlines, also known as SAS, is running a promotion through year’s end to celebrate its entry into the SkyTeam airline alliance, which also includes Delta and Air France. The carrier is giving away one million points in its EuroBonus loyalty program to anyone who flies on at least 15 SkyTeam airlines by Dec. 31. Those who fall short of the ultimate goal could still receive as many as 100,000 points depending on how many airlines they fly with.

This game of continental hopscotch has become something of a status symbol among travel-loyalty nerds. They have set online forums ablaze trading sample itineraries, booking tips and other hacks. Especially competitive fliers have set goals to see who can earn the points faster and cheaper than everyone else. Some plan to fly in one extended trip, while others have broken it into separate chunks.

Employees at the airline are placing bets on how many people will complete the challenge, with estimates ranging from five to 500, said Aron Backström, vice president of product and loyalty at SAS.

Richard Cherskov, a 50-year-old from Fort Lauderdale, Fla., already had a trip to Europe planned this fall that he realized he could mix into the SAS challenge.

He decided to go for it, swayed by the sheer number of points at stake. All but two of his flights will be in economy class. During his many flights, he plans to work remotely.

“I think that will keep me distracted and not have me focusing so much on my comfort," he says.

Corey Wong has already started his run. He says quality time with friends has made it more bearable. Wong, who lives in Hong Kong and works in transportation planning, convinced two college friends to join him. The trio bonded years ago during backpacking trips through China and Southeast Asia.

During one recent trip, the group returned to some of the places they had visited years ago. “We stayed in decent hotels this time," he says.

Fulfilling the challenge generally requires multiple ocean crossings. Travelers choose from 17 airlines, including major carriers like KLM and smaller ones like Romania’s Tarom or Xiamen Airlines in China.

A common strategy: identifying flights between two destinations outside an airline’s home market, letting fliers avoid longer, costlier trips farther afield. A Kenya Airways flight between Bangkok and Guangzhou, China has become popular for those on this quest.

Travelers doing the challenge say that building an ideal itinerary can take days. Potential pitfalls abound. Not all fare classes on a flight are eligible to earn EuroBonus miles. Airlines can change their schedules due to aircraft or crew constraints, potentially upending a carefully orchestrated string of flights.

Venturing outside the airport presents its own risks. After recently exploring Guangzhou, Peer Linder boarded the wrong subway and ended up on the opposite side of the city from the airport. A ride-share hustled him to the airport just 15 minutes before check-in for his flight closed.

Linder, who works for the travel website Travel-Dealz in Rostock, Germany, had never flown on many of the airlines he’s taking to complete the challenge. He has appreciated the variety of in-flight dining across the various carriers, including fried rice and seafood dishes on the Chinese airlines he has flown.

“It’s not the usual chicken or pasta from British Airways or Lufthansa," he says.

Industry analysts estimate the million-point haul to be worth north of $10,000 depending on how the rewards are used. To maximize the value, many travelers are trying to spend as little as possible on their flights, using a combination of credit-card points, frequent-flier miles and cash to book their trips. Most travelers anticipate spending between $2,000 and $4,000 on airfare, though it’s easy to spend far more depending on the flights and seats chosen.

Nick Lovell, a 21-year-old college student, says he expects to rely primarily on Chase and American Express points—between 190,000 and 210,000. (Some non-U.S. carriers charge far less for rewards travel, making this feasible.) To save even more, he plans to sleep in airport lounges or hostels when he has longer stretches between flights.

“I can handle it—I’m young," Lovell says.

Beyond cost, Lovell must also balance his travel with school. He plans to knock out multiple European airlines during a jam-packed trip over a weekend and another slew of airlines over his Thanksgiving break, much to his family’s chagrin.

Marty Paz, a 45-year-old who works in real estate and for an airfare-deals website called Notiflyr, used Turkey Day to his advantage. To get his wife on board, he suggested they use it as an excuse to travel to the U.S. from their home in Tel Aviv to visit her family for the holiday.

For another trip, Paz plans to visit a U.K. Costco to pick up bulk packs of diapers and baby wipes for his daughter. He is also considering bringing her with him on some travels through East Asia to give his wife some kid-free time.

Matthew Klint, the Los Angeles-based author of the blog Live and Let’s Fly, is bringing his 8-year-old son Augustine along for the global expedition so they each earn the million-point reward. Along the way, they hope to check out the pyramids in Egypt.

Augustine will still need to finish his homework during their flights.

“I’m going to have to pull him out of school for a week, and I feel somewhat guilty about that," Klint says. “He is only in second grade, so I think it’s totally worth it."

Write to Jacob Passy at jacob.passy@wsj.com