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 Walgreen (NYSE: WAG) for example. Since the late 1960s,Walgreen's share price has increased some 13,000%. But add in reinvested dividends, and total returns jump to nearly 36,000%:

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

There's no ambiguity here: Over time, Walgreen's share appreciation alone has paled in importance to the power of its reinvested dividends. The results resemble those of competitors CVS Caremark (NYSE: CVS) and Wal-Mart (NYSE: WMT); reinvested dividends skew both companies' total long-term returns overwhelmingly higher. If you're a shareholder, don't worry about daily share wobbles. Devote your attention those dividend payouts, and your commitment to reinvest them.

And how do Walgreen's dividends look? The company has paid a dividend every year since at least 1972. Its current yield -- 2.1% -- is not terribly high by market standards, but Walgreen has grown its dividend impressively, doubling per-share dividends since the recession began in 2007. Over the past five years, Walgreen's dividend has used up an average of just 30% of free cash from, meaning it's easily covered and free from the risk of any immediate cuts.

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.