(FORTUNE Magazine) - "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 (Research) 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 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, 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.

Next pitfall: Failing to build a culture of trust.

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Why dream teams fail:

• Signing too many all-stars
• Failing to build a culture of trust
• Tolerating competing agendas
• Letting conflicts fester
• Hiding from the real issues