Two years ago, Taj Hotels Resorts & Palaces (more formally, the Indian Hotels Co.)—known at home for its lavish accommodations, but an unfamiliar name to many Americans—arrived in the U.S. with a splash.

First, Taj picked up the right to operate and manage the Pierre, one of Manhattan’s most distinguished hotels, located just across Fifth Avenue from Central Park and for a long time a feather in the cap of the Four Seasons chain. Earlier this year, Taj struck in downtown Boston, purchasing a landmark Beaux-Arts building that had spent the previous 79 years as a Ritz-Carlton, for $170 million. [Author’s note: It was also the longest continuously operating Ritz-Carlton hotel.] In April, Taj announced its $58 million purchase of San Francisco’s century-old Campton Place Hotel, in Union Square, from Kor Hotel Group. (Read “The Hotel Collector.")

Taj isn’t the only deep-pocketed buyer that has recently been targeting so-called trophy hotels—properties that are luxurious, high-profile, and in prime locations and many of which are historic and have been owned or run by the same companies for decades but are now being swapped like so many high-priced baseball cards. Campton Place had sold for $44 million to Kor just a year and a half before Taj bought it. In 2005, a Dubai investment group purchased the Essex House, a Manhattan property dating from 1931, which had just been sold in 1999. Four of London’s most famous hotels changed hands three times in the past decade: The Blackstone Group and Colony Capital purchased the Savoy, the Berkeley, Claridge’s, and the Connaught for about $1 billion in 1998. In 2004, they sold the hotels to Quinlan Private for $1.4 billion. Quinlan then sold the Savoy to Prince al-Waleed bin Talal bin Abdul Aziz al-Saud of Saudi Arabia.

Sometimes the switch is barely noticeable to guests—a new flag out front, an extra word or two tacked onto the name—but in other cases, expensive and extensive renovations ensue.

Ty Warner, the Beanie Babies billionaire, who has been assembling a collection of high-profile properties—including the 500-acre San Ysidro Ranch in California; the 80-year-old Four Seasons Biltmore in Santa Barbara, California; and the I.M. Pei-designed Four Seasons New York—has put tens of millions of dollars into overhauls.

“The sense is that more of these hotels aren’t going to be built,” says Bjorn Hanson, lodging specialist at PricewaterhouseCoopers in New York. “Sites are not available. The artisanship isn’t the same. Many historic luxury hotels could never be replicated.” All this means that, over time, the properties will become even more valuable and possibly more profitable, even if the owner doesn’t immediately make money from the investment.

“There’s a ton of capital out there that needs to be invested, and for the first time ever, hotels are seen as good investments,” says Jeff Weinstein, editor in chief of Hotels and Hotels’ Investment Outlook, trade publications based in Oak Brook, Illinois. “Now that hotels have shown they are growing profits, they are selling at incredible multiples.”

The luxury segment, which saw the highest increase in average room rates in 2007, is growing quickly, Hanson says.

But profits aside, some of what motivates these high-profile hotel purchases comes down to vanity, Weinstein says. “The trophy properties are going to high-net-worth individuals”—and companies—“who want to own high-worth real estate.”

So which will be the next domino to fall—or to fall again at an even higher price? We polled the top executives of some of the industry’s biggest brands, including Ritz-Carlton and Fairmont Raffles, to find out what they would add to their hotel portfolios if money and current ownership were no object.

Some, like Simon Cooper, chief operating officer and president of Ritz-Carlton, selected other hotels. The Ciragan Palace in Istanbul, currently a Kempinski Hotels property, was his pick.

“I love Istanbul as a city,” Cooper says. “And when we developed our hotel there, I saw the Ciragan Palace. It’s just stunning. And how can you beat the location?” The hotel, which was the palace of the last Ottoman sultan, sits right on the Bosporus. And although Cooper has never stayed there and says he has “not a clue” as to its potential price, he covets it nonetheless.

“They don’t have to sell it to me,” he concludes whimsically. The Ritz “could just manage it.”

Indeed, desire is usually not rational. Raymond Bickson, of Taj, makes a characteristically outrageous choice.

“My dream acquisition would be Buckingham Palace,” he writes via email. “Taj has a long history of restoring palaces. While I’m sure Buckingham Palace is in excellent condition, I can’t help but think it would be even better under the Taj flag.”