FORTUNE — IBM turns 100 this month. Remarkably, IBM (IBM) has stayed vital and important for most of its history — except for that blip in the early-1990s when the company nearly collapsed. In 1911, the company had $800,000 in net income. In 2010, IBM’s net income was $14.8 billion. Its stock has appreciated about 40,000 times.

A lot of IBM’s success can be traced back to its earliest years and the actions of Thomas Watson Sr., who ran IBM from 1914 to 1952. Today’s entrepreneurs and CEOs could learn some lessons from Watson, especially if they want to build a company for the ages.

So here are five lessons from Watson on making a 100-year company.

1. At the start, convince the troops you’re a company of destiny, even if that seems crazy.

IBM began life as Computing-Tabulating-Recording Co. (C-T-R), a rag-tag amalgamation of pseudo-information companies assembled in an acquisition by Wall Street financier Charles Flint in 1911. C-T-R was flailing when it hired Watson to take charge in 1914. Morale was down. The division managers fought each other. So what did Watson do? He told his amazed employees that they were building a world-class, important company.

In verbatim notes from Watson’s first meeting with 30 senior executives, Watson tells them to sell their products hard, “always having in mind that this business has a great future, and that everybody has a bearing on the future of this business.” He repeated messages of grandeur time and again — and renamed little C-T-R with the expansive name of International Business Machines. Eventually, employees believed him, and they felt like they didn’t just have a job — they were on a mission. You still find the same attitude in the halls of IBM today.

2. Build a cult-like culture that people either buy into, or run away from.

Watson was among the first CEOs to really understand that a strong company — like a nation — is built on a culture and shared set of values. And then Watson took it to an extreme, creating a culture that was so quirky, it tightly bonded people who joined — and ejected people who didn’t buy in.

The quirks included the famous THINK signs, a no-alcohol policy (IBM today still won’t pay for a traveling executive’s glass of wine with dinner), a dress code of stiff white shirts, and a tradition of group-singing of songs about IBM. The culmination of Watson’s odd culture was an annual event in the mid-twentieth century that brought thousands of the company’s top salesman to a hillside in Endicott, N.Y. — and housed them in tents.

While it’s hard to find a young tech company today that’s that quirky, Netflix is one example of a strong, unusual culture — and as a result has one of the lowest employee turnover rates in Silicon Valley.

3. Bet the company once in a while.

In the 1930s, with the Depression raging, Watson rolled the dice. While competitors laid off workers, closed factories and cut R&D, Watson refused to do any of that and in fact built a state-of-the-art lab in Endicott in 1933. He wanted to be ready for an explosion of demand when the economy turned around. But as the Depression lingered, IBM’s finances were nearly in ruin.

Then, in 1936, the Social Security Act passed, creating the single biggest information problem — tracking all those paychecks — for government and business to date. Only one company was in a position to handle it: IBM. It had machines ready, factories running, and new technology. IBM’s business rocketed.

Watson and his son, Thomas Watson Jr., would go on to bet the company several times, including perhaps IBM’s most daring bet, the System/360 computer in the 1960s. The 360 was like Apple’s bet on the iPhone — if Apple stopped making every other product at the same time.

4. Make people talk about you.

In Watson’s day, most of the population never touched and didn’t understand IBM’s back-office computing machines. So Watson continually found ways to make the public take notice. In 1939, he funded a grand “IBM Day” at the World’s Fair in New York. In the 1940s, he set up one of IBM’s first electronic computers in the lobby of corporate headquarters on Madison Avenue, so everyone passing by could see it in operation.

IBM has never forgotten the value of such acts. In the 1990s, it got headlines when Deep Blue beat world champion Gary Kasparov at chess. This year, IBM’s Watson computer beat two all-time champs in a Jeopardy! match on TV.

5. Hand off to a successor who is better than you.

This may be the hardest trick of all — but it’s crucial to building a 100-year company. No leader is ever going to stick around for a century. That first successor has to be an equally bold leader, who perhaps can even overshadow the original company builder. The problem is, great company builders are often powerful personalities who drive away other strong personalities below them.

Watson got lucky. He had a son, Tom Watson Jr., who was as strong-willed and gifted as the father. The two of them fought like crazy, yet Tom didn’t leave. After running IBM for almost 40 years, Watson handed leadership to Tom — who quickly plunged IBM into the new era of electronic computing. The arrival of electronics allowed Tom Watson to build on the past, yet toss out what had become stale — in this case, IBM’s reliance on punched-card machines.

This is where a lot of companies stumble on the path to 100 years. Microsoft (MSFT) needed a bold successor to Bill Gates who could break from the company’s Windows and PC past and take it to an Internet future. Steve Ballmer couldn’t do it. Apple (AAPL_ after Steve Jobs will need a new leader who’s willing, as they say, to think different from Jobs.

Obviously, it’s not easy to be a vibrant company for most of 100 years. It takes a cultural foundation at the start, some big bets and luck along the way, and a great second act when it’s time for the first successor to take charge. Keep those things in mind, and it might be possible to guess which of today’s companies will be around at 100.