The best thing about the two-week dream vacation Andrew Vojslavek and his wife took to the British Virgin Islands last spring wasn’t the crystal clear blue waters or white sands. It wasn’t their private bungalow or the chance to pursue their favorite recreational activity right on the beach.

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“Every day we’d wake up and go rock climbing, come back and have breakfast, go snorkeling, then go climbing again and just enjoy the views,” recalled Vojslavek.

But the best thing about Vojslavek’s vacation was that his employer picked up the tab.

Vojslavek, 28, is the sales director at FullContact, a Denver-based software solutions company that offers a benefit it calls a “paid paid” vacation. Once a year, FullContact employees are entitled to a flat $7,500 payment to be used toward a vacation of their choice.

The only requirement? They are not allowed to check email or call the office while they’re away. 

“It’s funny,” said Vojslavek. “When you tell people about this benefit, they look at you like you’re complete crazy and can’t believe it’s even a real thing.”

And if the “paid paid” vacation isn’t enough, FullContact employees can also take an unlimited number of vacation days throughout the year.

FullContact isn’t the only company offering unlimited days off as an employee benefit. Among the growing number of others are Netflix, Evernote, Motley Fool and the Gilt Groupe, said Roger Dow, president and CEO of the U.S. Travel Association, the Washington, D.C.-based umbrella organization representing all segments of travel in America.

Richard Branson, founder and CEO of Virgin Group, recently blogged that his company is experimenting with unlimited vacation time. “And Expedia has eliminated its vacation policy altogether,” said Dow. “We’re seeing this as the beginning of a trend that is starting on the West Coast at tech companies.”

Unlimited vacation time is particularly appealing to millennials like Vojslavek. “Millennials tend to spend their money on experiences rather than material goods,” Dow said. “They’d rather have a less expensive car and more money to travel. We hear that all the time in our research.”

It would be a boon for the travel industry if the millennials’ priorities started rubbing off on other segments of the population, Dow said, but that would require a seismic shift in the way Americans regard vacation time.

A 2013 report by the Center for Economic and Policy Research, a Washington think-tank, found that "The United States is the only advanced economy that does not guarantee its workers any paid vacation time." As a result, the report found, ours is a “no-vacation nation” where almost one in four Americans receives no paid vacation and no paid holidays.

“And of the people who do get paid time off, 40 percent leave an average of 3.2 days untaken,” Dow said. “That translates to 429 million vacation days that Americans leave on the table every year.”

Indeed, research earlier this month by Skift, the travel-industry intelligence website, revealed that about half of Americans hadn’t yet taken a single day off this year.

Company culture is often to blame, said Dow, whose association’s “Overwhelmed America” study revealed a disconnect between company policies and day-to-day realities.

“While 90 percent of both bosses and employees said that travel was important to recharging batteries, to health and to relationships, 67 percent of employees report that their bosses don’t encourage taking vacations or give mixed messages about taking time off,” he said.

Consequently, Americans often are nervous about being away from the office for too long at a time, and they are increasingly likely to extend a weekend than take a full week off. “People are trying to use their days judiciously to get the most out of their vacation time,” said Dow. “And then the American work martyr complex comes into play.”

The term “work martyr” emerged in the “Overwhelmed America” study. Forty percent of respondents said they don’t take all their accrued vacation time because they’re afraid of the mountain of work they’ll have to face when they get back. Another 35 percent said that, due to downsizing or restructuring, they were the only one who could do their job. And almost a quarter of respondents said they were afraid of losing their jobs if they took a vacation.

“I’d like to see the One More Day campaign be successful,” said Dow, referring to MasterCard’s TV ad campaign, which aims to motivate Americans to take one vacation day that would otherwise remain unused. People who take a social pledge using the hashtag #OneMoreDaySweeps have the chance to win a grand prize trip for four, valued at $25,000, to a destination of their choice.

If people start taking their one more day, it could potentially inject $70 billion into the economy,” Dow said. “And we think the travel industry is in a position to get about half of it.”

One segment that needs no convincing is the millennials, who are the least likely demographic segment to leave vacation days unused. “The millennials will be big leaders in this trend of unlimited vacation days,” Dow said. “Organizations that want to attract and keep young talent will increasingly adopt this as a benefit.”

Vojslavek agrees. “The beautiful thing about the unlimited vacation is that you want to make sure you’re always putting your best foot forward for your employer,” he said. “And if you feel you need to take a few days off in order to come back recharged and better, it’s wonderful if your employer supports that.”

Suzanne Rowan Kelleher is the family vacations expert at About.com.