(FORTUNE Magazine) - In what universe is it even conceivable that the United States could fail to reach the semifinals of something called the World Baseball Classic? Not only fail to win, but could field a team that included Roger Clemens, Derek Jeter, Alex Rodriguez, and Johnny Damon and then lose games to Mexico, South Korea, and - wait for it -Canada? Yet it happened this year.

How could a movie starring Brad Pitt, George Clooney, Catherine Zeta-Jones, and Julia Roberts, directed by Steven Soderbergh, get tepid reviews and gross less worldwide than the star-free My Big Fat Greek Wedding? That movie was Ocean's Twelve.

And how could a FORTUNE 500 company run by a brilliant former McKinsey consultant, paying fat salaries to graduates of America's elite business schools, dissolve into fraud and bankruptcy? It happened at Enron. If someone tells you you're being recruited onto a dream team, maybe you should run. In our team-obsessed age, the concept of the dream team has become irresistible. But it's brutally clear that they often blow up. Why? Because they're not teams. They're just bunches of people.

A look at why so many dream teams fail, and why so many of the most successful teams consist of individuals you've never heard of, yields insight into the essential nature of winning organizations. As always when the subject is the real-world behavior of human beings, the takeaway includes things we always knew - even though we rarely behave as if we do.

The most important lesson about team performance is that the basic theory of the dream team is wrong. You cannot assemble a group of stars and then sit back to watch them conquer the world. You can't even count on them to avoid embarrassment. The 2004 U.S. Olympic basketball team consisted entirely of NBA stars; it finished third and lost to Lithuania.

By contrast, the 1980 hockey team that beat the Soviets at the Lake Placid Olympics was built explicitly on anti-dream-team principles. Coach Herb Brooks, who died in 2003, based his picks on personal chemistry. In the story's movie version, Miracle, Brooks' assistant looks at the roster and objects that many of the country's greatest college players were left out (professionals were not eligible to play then). To which Brooks responds with this essential anti-dream-team philosophy: "I'm not lookin' for the best players, Craig. I'm lookin' for the right players."

To see why dream teams so often disappoint, let's consider the most common paths to failure.

Signing too many all-stars.

"Some of the worst teams I've ever seen have been those where everybody was a potential CEO," says David Nadler, chief of the Mercer Delta consulting firm, who has worked with executive teams at top global companies for more than 30 years. "If there's a zero-sum game called succession going on, it's very difficult to have an effective team."

Chemistry and culture are key. Henry Ford II successfully brought in the Whiz Kids, a pre-assembled team of U.S. Army managerial stars that included Tex Thornton, Robert McNamara, and others, when he sensed that Ford needed a revolution after World War II. Young and iconoclastic, they had a record of working together effectively, and they did well at Ford, helping it to cash in on the postwar boom. But 50 years later when CEO Jacques Nasser correctly decided that Ford (Research) needed another revolution, he stuck with the old-guard team already in place. Like most old guards, they weren't ready for a real revolution, and when push came to shove, Nasser got ejected. More seriously for Ford, the revolution didn't happen.

For a notably successful method of choosing team members, look at Worthington Industries (Research), the Ohio-based steel processor. When an employee is hired to join a plant-floor team, he works for a 90-day probationary period, after which the team votes to determine whether he can stay. The system works because much of the team's pay is based on performance, so members are clear-eyed and unsparing in evaluating a new candidate's contribution. Worthington's CEO, John McConnell, could be talking about teams at any level when he says, "Give us people who are dedicated to making the team work, as opposed to a bunch of talented people with big egos, and we'll win every time."

That's the philosophy that powers teams such as basketball's Detroit Pistons and especially football's New England Patriots. The Pats have won three Super Bowls in the past five years with few stars and a quarterback, Tom Brady, who was the 199th pick. The Washington Redskins, by contrast, have bought star after star - and floundered.

Failing to build a culture of trust.

Read the extensive literature on team effectiveness, or talk to people on teams in sports, business, or elsewhere, and it always comes down to this: Trust is the most fundamental element of a winning team. If people think their teammates are lying, withholding information, plotting to knife them, or just incompetent, nothing valuable will get done. The team doesn't create synergy. It creates "dysergy" - two plus two equals three, with luck.

So dream teams are in trouble right from the start because team members may have particular reasons to be distrustful. In sports settings they are often brought together only briefly from teams that spend the rest of the year trying to beat each other. Even if team members can set aside that antagonistic mindset, they rarely have time to develop confidence in one another's behavior. It's similar in business: Even if team members aren't battling for the next promotion, someone is always getting moved or stolen away. "A major problem is that people are transient," says consultant Ram Charan. Especially on an all-star team, "there's all the headhunting, and there's a constant tug to have people pulled out of the team. Instability is a major issue." That's a big problem because trust, by its nature, builds slowly.

Many companies try to speed the trust-building process. In the '80s there was a virtual epidemic, often in woodsy corporate off-sites, of people falling backward off tables into the arms of co-workers as a way of learning trust. Maybe it even helped. Today consultants have developed many additional exercises that involve people sharing personal stories or revealing their personality type, based on the valid insight that reciprocal vulnerability is the beginning of trust. But the process can be rushed only so much.

In fact, trust is so fragile and so laboriously created that it may never extend very far in a top-level team. "Building a really high-performing executive team at the highest level is a mirage," says a management consultant who doesn't want to be quoted because this particular message is a downer. "When such teams do exist, they'll consist mostly of two people, maybe three." It's just too hard to build trust more extensively at the top level, where everyone is supposedly a star.

And sure enough, the legendary top executive teams are almost always pairs. Think of Roberto Goizueta and Donald Keough at Coca-Cola (Research) in the '80s and '90s, or Tom Murphy and Dan Burke at Capital Cities/ABC from the '60s to the '90s, or Reuben Mark and Bill Shanahan at Colgate-Palmolive (Research) for two decades until last year, or Warren Buffett and Charlie Munger at Berkshire Hathaway (Research) from the '60s to today. No one would have called those pairs dream teams back when they got together; at the time, most people had never heard of them.

Maybe you noticed something else about those teams: Each consisted of a boss who became famous and a much less famous No. 2 who devoted his career to the success of the enterprise. In every case, though, they developed deep trust over many years and produced outstanding results.

Tolerating competing agendas.

You don't often find examples of the best and worst executive teams involving the same person, but consider the case of Michael Eisner. For the first ten years of his reign at Disney (Research), he and COO Frank Wells formed one of corporate America's great teams. On their watch, Disney revived its glorious animation tradition, and the movie business flourished. Eisner and Wells could take credit for saving a storied company - and making shareholders rich. This productive partnership ended suddenly and terribly when Wells died in a 1994 helicopter crash.

Eisner then formed one of the most famously disastrous teams in recent history, bringing in uber-agent Michael Ovitz as president. He lasted only 14 months. In the extensive postmortems, the overriding theme is of conflicting business and personal agendas. Ovitz wanted to buy a major stake in Yahoo (Research), expand Disney's book and record businesses, and buy an NFL franchise, among other big ideas that Eisner dismissed as off-strategy. Ovitz also seemed to have notions of his own future - he spent $2 million remodeling his office - that did not sit well with Eisner. Bottom line: team failure, at tremendous cost to Disney in both money and prestige.

It is many a father's dream to team up with his sons, but family businesses can find it particularly difficult to unpick the personal from the corporate. That is one part of the dynamic that operated at Adelphia, the cable company founded by John Rigas. Even after it went public, Rigas and his sons operated it as if were still a family concern - for example, paying for private expenses from corporate funds. They got nailed, and Adelphia went bankrupt in 2002.

The challenge is to keep the inevitable personal agendas from becoming destructive. That's part of the leader's job. For example, Ameritech in the '90s had an all-star team of top executives that included Richard Notebaert, future CEO of Ameritech, Tellabs, and Qwest, and Richard Brown, future CEO of Cable & Wireless and EDS. Michigan business school professor Noel Tichy, who was advising the company on leadership development at the time, recalls that CEO Bill Weiss told the team bluntly every week that if he caught anybody trying to undermine the others, the guilty party would be fired. It worked.

Letting conflicts fester.

Col. Stas Preczewski, coach of the Army crew at West Point a few years ago, faced a baffling problem. Through extensive testing, he had developed objective criteria to rank his rowers. He then put the eight best - his dream team - in the varsity boat and the eight others in the junior varsity boat. The problem: The JV beat the varsity two-thirds of the time. The situation, as explained in a Harvard Business School case, was that the varsity was full of resentment over who was contributing most, while the JV, feeling they had nothing to lose, supported one another happily.

One day Preczewski lined up the varsity crew in four pairs. He told them they were to wrestle - no punching - for 90 seconds. There were no clear winners: Each man was discovering that his opponent was just as strong and determined as he was. Preczewski then had them change opponents and wrestle again. By the third round they were choosing their own opponents - "One guy would point at another and say, 'You!'" Preczewski says. Finally, one of the rowers started laughing, and they all piled into a general brawl. Eventually someone said, "Coach, can we go row now?" From then on, the varsity boat flew.

You probably can't order members of an executive team to wrestle, tempting though it may be. But bringing tensions out into the open and then resolving them is one of the team leader's most important jobs.

Hiding from the real issues.

"Put the fish on the table," says George Kohlrieser, a professor at the International Institute for Management Development in Switzerland. You've got to go through the "smelly, bloody process of cleaning it," but the reward is "a great fish dinner at the end of the day." Most people don't want to be the one who puts the proverbial fish on the table. "There's a veneer of politeness," says consultant David Nadler, "or unspoken reciprocity - we won't raise our differences in front of the boss." Consultant Ram Charan describes a $12 billion division of ABB that was headed for bankruptcy, in part because of "its culture of polite restraint. People didn't express their honest feelings" about the most important issues. The unit's leader turned it around by insisting that team members say what was on their minds.

Jack Welch was one of the great champions of putting the fish on the table - facing reality, as he says. GE's dream team was and is the Corporate Executive Council, which used to meet at headquarters in a formal atmosphere with rehearsed presentations and little real discussion. Welch moved the meetings off-site, forbade prepared presentations and jackets and ties, and lengthened the coffee breaks to encourage informal discussion, among other changes. At GE they call this "social architecture" and believe it was a critical element of Welch's success.

In business, dream teams are usually part of some rescue fantasy, not the real world. "Be prepared to have an imperfect set," says Charan. "Then you've got to devote your energy to getting them to synchronize. It's very time consuming. It taxes your patience." It's life.

To avoid seducing yourself into thinking all your problems might be vaporized by assembling a dream team, resolve now to accept this fact: There was only one Dream Team, and that was the 1992 U.S. Olympic basketball team. Michael Jordan, Magic Johnson, Larry Bird, Charles Barkley, Patrick Ewing - it was a one-time event. (And remember, Bird and Magic, the veteran co-captains, both had reputations as team players.) For the rest of us, putting together a few talented people who will work honestly and rigorously for something greater than themselves - that's more than enough of a dream.