I took my first investing class as a teenager, and one moment stands out in my memory. A fellow student asked the instructor, a stockbroker, about dividends.

"Dividends?" he asked. "I'm trying to make my clients wealthy. You don't do that waiting for tiny checks in the mailbox every quarter."

Even then, I had enough horse sense to know he was wrong. Paying attention to dividends is exactly how you become wealthy over time.

Wharton professor Jeremy Siegel made a wonderful discovery in his book The Future for Investors. The greatest long-term returns typically don't come from the most innovative companies, or even companies with the highest earnings growth. They come from companies that happen to crank out dividends year after year. Simply put, since the 1950s, "the portfolios with higher dividend yields offered investors higher returns."

Market commentary regularly centers around price gyrations, yet dividends have historically accounted for more than half of total returns.

Reinvest those dividends, and your results become even greater. Take American Express (NYSE: AXP), for example. Since the late 1970s, American Express' shares have increased 1,500%. But add in reinvested dividends, and total returns jump to more than 5,000%:

Source: Capital IQ, a division of Standard & Poor's.

There's no ambiguity here: Over time, American Express' share appreciation alone has paled in importance to the power of its reinvested dividends. A meaningful dividend yield is one benefit AmEx holds over competitors Visa (NYSE: V) and MasterCard (NYSE: MA). If you're a long-term shareholder, don't worry about daily share wobbles. Devote your attention those dividend payouts, and your commitment to reinvest them.

And how do those dividends look? AmEx was one of the only large financial companies to make it through the financial crisis without cutting its dividend -- a testament to its strength and management's commitment to shareholders. The company has paid a dividend every quarter since at least 1989. Its current yield -- 1.4% -- isn't high by market standards, but is superior to nearly all other large financial-services companies, many of whom are still barred from paying significant dividends at all. AmEx's dividend uses up a trivial portion of its free cash flow, keeping its payout fairly safe from cuts unless struck by another financial crisis -- which one can never rule out.

To earn the greatest returns, get your priorities straight. What the market does is less important than what your company earns. What your company earns is less important than how much it pays out in dividends. And what it pays out in dividends is less important than whether you reinvest those dividends.

Add American Express to My Watchlist.

Fool contributor Morgan Housel doesn't own shares of any of the companies mentioned in this article. Follow him on Twitter @TMFHousel. Motley Fool newsletter services have recommended buying shares of Visa. 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 Motley Fool has a disclosure policy.