Every investor dreams of getting in early on a stock that keeps going up for decades. Yet while hindsight easily reveals companies that have managed to stand the test of time, it's a lot harder to guess today which companies will survive well into the future.

But there's a key element that any long-lived company manages to master. In order to stay relevant throughout the decades, every company must keep innovating. No matter how simple a company's business model may seem, it must constantly evolve to adapt itself to successive generations.

A look at economic history
It's easy to think of blue-chip stalwarts as unchanging bellwethers of the economy. But when you take a closer look at companies over the long haul, you'll see just how much many seemingly stable businesses have changed over the years.

For instance, IBM (NYSE: IBM) has gone from making adding machines and typewriters to reinventing itself as a computing legend, developing the machines that have gone on to dominate the business world for decades. Yet like pro athletes retiring at the top of their game, IBM then went on to discard much of its emphasis on hardware in favor of higher-margin information technology consulting services.

You'll see similar reinventions at many companies. AT&T (NYSE: T) is trying to remake itself into a mobile giant after relying on landline-related businesses throughout much of the 20th century. Coca-Cola (NYSE: KO) is still firmly ensconced in the beverage business, but it now offers a huge variety of drinks targeted at completely different demographics for a wide range of purposes.

In contrast, companies that have failed to innovate have often found themselves on the short end of the survival stick. Polaroid and Eastman Kodak (NYSE: EK) both stood atop the world of film, but neither has thus far been able to bridge the gap successfully to produce dominance in digital imagery, despite a few successes for Kodak. Scores of other companies have ended up on the scrap heap because they couldn't make the leap beyond their niches.

Tomorrow's long-lived stocks
If anything, the fast pace of today's business world requires even more innovation. That's why in a search for the stalwarts of tomorrow, you have to see consistent dedication to pushing the envelope.

I see that kind of innovation at Amazon.com (Nasdaq: AMZN). Obviously, most people are familiar with Amazon primarily for its command of the online retail market. But within retail, innovations like bringing on third-party sellers and offering paid memberships for free fast shipping have pushed Amazon's business to a whole new level. The vertical integration of selling its own e-reader to promote electronic book sales has already produced successes, and it opens the door to potential competitors to the red-hot tablet market. And the company's almost completely unrelated foray into cloud computing reveals that Amazon is ready to move in unexpected directions, as long as they hold promise of a profitable future.

Dig deep, and you can find several similar companies that have demonstrated greater vision than their peers. While its competitors were busy playing catch-up in the U.S. travel market, priceline.com (Nasdaq: PCLN) made inroads in international destinations, giving itself a huge advantage as traveling abroad becomes not only a personal luxury, but also a necessary part of a functional global economy. And as most casino companies focused on building in overcrowded Las Vegas, Las Vegas Sands (NYSE: LVS) was among the first to see the potential of Macau -- a move that arguably saved the company during the recession.

Look for innovation
Of course, not all innovation succeeds -- just think back to all the failed Internet companies of the early 2000s to see plenty of examples of novelty without value. But without an innovative impulse, even the best companies stagnate and eventually fall under their own weight. Only through reinvention can a business hope to stand the test of time and become a stock for the ages.

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Fool contributor Dan Caplinger won't stop thinking about tomorrow. He doesn't own shares of the companies mentioned in this article. Coca-Cola and AT&T are Motley Fool Inside Value selections. Amazon.com and priceline.com are Motley Fool Stock Advisor recommendations. Coca-Cola is a Motley Fool Income Investor selection. The Fool owns shares of Coca-Cola and IBM. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Fool's disclosure policy sends you back to the future.