(FORTUNE Magazine) – CEOs used to have an important rite of passage: When a company reached a certain level of grandeur, the chief executive hired a major architect to design a new headquarters, a trophy building symbolizing the company's financial might and corporate style. The skyline of every major American city is adorned with these wonders. Chicago has the Sears Tower. San Francisco boasts the Transamerica Pyramid. New York City has monuments erected by Woolworth, Citicorp, Seagram, and Chrysler, to name just a few.

Now corporate America's love affair with the trophy building is waning. Obviously there's a concern that after Sept. 11, buildings calling attention to themselves may be terrorist targets. Earlier this year DEGW, a consulting and design firm, surveyed real estate executives at large U.S. companies and found 41% were less interested in occupying high-profile buildings after Sept. 11. Nearly a fifth said they would be happier in "anonymous" buildings. Morgan Stanley, for example, passed on plans to move into a posh midtown tower, instead relocating hundreds of employees to Jersey City, where the tony firm is just another tenant in a nondescript building.

It would be a mistake, however, to blame Sept. 11 entirely for the decline of trophy buildings. Matthew Cullen, head of real estate for GM and chairman of CoreNet Global, an association of top real estate executives, says companies began forsaking trophy buildings nearly a decade ago when technological advances like the Internet and cellphones allowed employees to work anywhere, lessening the need for a fancy tower.

Sandy Apgar, a director at the Boston Consulting Group who advises corporations on real estate, sees the same trend. He counsels clients to follow the lead of AT&T, which cut costs and increased productivity in the early '90s when it left its posh, Philip Johnson-designed Manhattan headquarters, moved its executive offices to the Jersey suburbs, and encouraged employees to telecommute. Sept. 11, says Apgar, has only accelerated things. Though a handful of companies like Ernst & Young and Reuters have recently moved into trophy-worthy digs, "the age of the corporate-icon building is passing," he says. "One of the great challenges facing the real estate industry is how to rethink and reuse the traditional corporate headquarters building for other purposes. I know some people who are thinking, very quietly to be sure, about converting buildings in New York and elsewhere into condos." Some companies--in particular, Random House and AOL Time Warner, parent of FORTUNE's publisher--are relinquishing the top floors of their under-construction Manhattan trophy buildings so that they can be sold as luxury condominiums rather than set aside for executive offices. That tells you how much things have changed.

So is this the end of a great corporate tradition? Probably not. Trophy buildings go up in boom times, not in downturns. Merrill Lynch recently noted that there was currently a "complete absence of demand" for office space and expected paralyzing market conditions to last at least though 2003. However, once the economy picks up, that sentiment may change. For all their downsides, trophy buildings offer CEOs a form of immortality. Few of the cars built by Walter Chrysler in the '20s survive, but the art deco spire he commissioned still looms majestically over Manhattan. You'll never make history for moving your employees into a nondescript suburban office building.