Few events arouse more teenage angst than the springtime arrival of college rejection letters. With next fall's college freshman class expected to approach a record 2.9 million students, hundreds of thousands of applicants will soon be receiving the dreaded letters.

Teenagers who face rejection will be joining good company, including Nobel laureates, billionaire philanthropists, university presidents, constitutional scholars, best-selling authors and other leaders of business, media and the arts who once received college or graduate-school rejection letters of their own.

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Both Warren Buffett and "Today" show host Meredith Vieira say that while being rejected by the school of their dreams was devastating, it launched them on a path to meeting life-changing mentors. Harold Varmus, winner of the Nobel Prize in medicine, says getting rejected twice by Harvard Medical School, where a dean advised him to enlist in the military, was soon forgotten as he plunged into his studies at Columbia University's med school. For other college rejects, from Sun Microsystems co-founder Scott McNealy and entrepreneur Ted Turner to broadcast journalist Tom Brokaw, the turndowns were minor footnotes, just ones they still remember and will talk about.

Rejections aren't uncommon. Harvard accepts only a little more than 7% of the 29,000 undergraduate applications it receives each year, and Stanford's acceptance rate is about the same.

"The truth is, everything that has happened in my life...that I thought was a crushing event at the time, has turned out for the better," Mr. Buffett says. With the exception of health problems, he says, setbacks teach "lessons that carry you along. You learn that a temporary defeat is not a permanent one. In the end, it can be an opportunity."

Famous 'Rejects' Warren Buffett Bloomberg News; Buffett family photo (inset) Chairman of Berkshire Hathaway Inc.

After Harvard Business School said no, everything 'I thought was a crushing event at the time, has turned out for the better.' Meredith Vieira Getty Images; NBC Universal (inset) 'Today' show co-host

Had she not been rejected by Harvard, she doubts she would have entered television journalism. Lee Bollinger Bryan Derballa for The Wall Street Journal; Baker City High School (inset) Columbia University president

To 'allow other people's assessment of you to determine your own self-assessment is a very big mistake.' Harold Varmus Bryan Derballa for The Wall Street Journal; Harold Varmus (inset) Nobel laureate in medicine

Rejected twice by Harvard's medical school. One dean there chastised him and advised him to enlist in the military. Ted Turner Bloomberg Entrepreneur

Rejected by Princeton and Harvard. 'I want to be sure to make this point: I did everything I did without a college degree.' John Schlifske Kevin J. Miyazaki for The Wall Street Journal President of Northwestern Mutual

Lesson he learned from Yale's rejection helped him years later counsel his son, Dan (standing), who was rejected by Duke. Tom Brokaw Getty Images Broadcast journalist

Harvard rejection prompted him to settle down and stop partying. 'The initial stumble was critical in getting me launched.'

Mr. Buffett regards his rejection at age 19 by Harvard Business School as a pivotal episode in his life. Looking back, he says Harvard wouldn't have been a good fit. But at the time, he "had this feeling of dread" after being rejected in an admissions interview in Chicago, and a fear of disappointing his father.

As it turned out, his father responded with "only this unconditional love...an unconditional belief in me," Mr. Buffett says. Exploring other options, he realized that two investing experts he admired, Benjamin Graham and David Dodd, were teaching at Columbia's graduate business school. He dashed off a late application, where by a stroke of luck it was fielded and accepted by Mr. Dodd. From these mentors, Mr. Buffett says he learned core principles that guided his investing. The Harvard rejection also benefited his alma mater; the family gave more than $12 million to Columbia in 2008 through the Susan Thompson Buffett Foundation, based on tax filings.

The lesson of negatives becoming positives has proved true repeatedly, Mr. Buffett says. He was terrified of public speaking—so much so that when he was young he sometimes threw up before giving an address. So he enrolled in a Dale Carnegie public speaking course and says the skills he learned there enabled him to woo his future wife, Susan Thompson, a "champion debater," he says. "I even proposed to my wife during the course," he says. "If I had been only a mediocre speaker I might not have taken it."

Columbia University President Lee Bollinger was rejected as a teenager when he applied to Harvard. He says the experience cemented his belief that it was up to him alone to define his talents and potential. His family had moved to a small, isolated town in rural Oregon, where educational opportunities were sparse. As a kid, he did menial jobs around the newspaper office, like sweeping the floor.

Mr. Bollinger recalls thinking at the time, "I need to work extra hard and teach myself a lot of things that I need to know," to measure up to other students who were "going to prep schools, and having assignments that I'm not." When the rejection letter arrived, he accepted a scholarship to University of Oregon and later graduated from Columbia Law School. His advice: Don't let rejections control your life. To "allow other people's assessment of you to determine your own self-assessment is a very big mistake," says Mr. Bollinger, a First Amendment author and scholar. "The question really is, who at the end of the day is going to make the determination about what your talents are, and what your interests are? That has to be you."

Others who received Harvard rejections include "Today" show host Meredith Vieira, who was turned down in 1971 as a high-school senior. At the time, she was crushed. "In fact, I was so devastated that when I went to Tufts [University] my freshman year, every Saturday I'd hitchhike to Harvard," she says in an email. But Ms. Vieira went on to meet a mentor at Tufts who sparked her interest in journalism by offering her an internship. Had she not been rejected, she doubts that she would have entered the field, she says.

And broadcast journalist Tom Brokaw, also rejected as a teenager by Harvard, says it was one of a series of setbacks that eventually led him to settle down, stop partying and commit to finishing college and working in broadcast journalism. "The initial stumble was critical in getting me launched," he says.

Dr. Varmus, the Nobel laureate and president of Memorial Sloan-Kettering Cancer Center in New York, was daunted by the first of his two turndowns by Harvard's med school. He enrolled instead in grad studies in literature at Harvard, but was uninspired by thoughts of a career in that field.

After a year, he applied again to Harvard's med school and was rejected, by a dean who chastised him in an interview for being "inconstant and immature" and advised him to enlist in the military. Officials at Columbia's medical school, however, seemed to value his "competence in two cultures," science and literature, he says.

If rejected by the school you love, Dr. Varmus advises in an email, immerse yourself in life at a college that welcomes you. "The differences between colleges that seem so important before you get there will seem a lot less important once you arrive at one that offered you a place."

Similarly, John Schlifske, president of insurance company Northwestern Mutual, was discouraged as a teenager when he received a rejection letter from Yale University. An aspiring college football player, "I wanted to go to Yale so badly," he says. He recalls coming home from school the day the letter arrived. "Mom was all excited and gave it to me," he says. His heart fell when he saw "the classic thin envelope," he says. "It was crushing."

Yet he believes he had a deeper, richer experience at Carleton College in Minnesota. He says he received a "phenomenal" education and became a starter on the football team rather than a bench-warmer as he might have been at Yale. "Being wanted is a good thing," he says.

He had a chance to pass on that wisdom to his son Dan, who was rejected in 2006 by one of his top choices, Duke University. Drawing on his own experience, the elder Mr. Schlifske told his son, "Just because somebody says no, doesn't mean there's not another school out there you're going to enjoy, and where you are going to get a good education." Dan ended up at his other top choice, Washington University in St. Louis, where he is currently a senior. Mr. Schlifske says, "he loves it."

Rejected once, and then again, by business schools at Stanford and Harvard, Scott McNealy practiced the perseverance that would characterize his career. A brash economics graduate of Harvard, he was annoyed that "they wouldn't take a chance on me right out of college," he says. He kept trying, taking a job as a plant foreman for a manufacturer and working his way up in sales. "By my third year out of school, it was clear I was going to be a successful executive. I blew the doors off my numbers," he says. Granted admission to Stanford's business school, he met Sun Microsystems co-founder Vinod Khosla and went on to head Sun for 22 years.

Paul Purcell, who heads one of the few investment-advisory companies to emerge unscathed from the recession, Robert W. Baird & Co., says he interpreted his rejection years ago by Stanford University as evidence that he had to work harder. "I took it as a signal that, 'Look, the world is really competitive, and I'll just try harder next time,'" he says. He graduated from the University of Notre Dame and got an MBA from the University of Chicago, and in 2009, as chairman, president and chief executive of Baird, won the University of Chicago Booth School of Business distinguished corporate alumnus award. Baird has remained profitable through the recession and expanded client assets to $75 billion.

Time puts rejection letters in perspective, says Ted Turner. He received dual rejections as a teenager, by Princeton and Harvard, he says in an interview. The future America's Cup winner attended Brown University, where he became captain of the sailing team. He left college after his father cut off financial support, and joined his father's billboard company, which he built into the media empire that spawned CNN. Brown has since awarded him a bachelor's degree.

Tragedies later had a greater impact on his life, he says, including the loss of his father to suicide and his teenage sister to illness. "A rejection letter doesn't even come close to losing loved ones in your family. That is the hard stuff to survive," Mr. Turner says. "I want to be sure to make this point: I did everything I did without a college degree," he says. While it is better to have one, "you can be successful without it."

Write to Sue Shellenbarger at sue.shellenbarger@wsj.com