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 the gains get even greater. Take Buckeye Partners (NYSE: BPL), for example. Since the late 1980s, the company's share price has increased 540%. But add in reinvested dividends, and total returns jump to over 4,000%:

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

There's no ambiguity here: Over time, Buckeye's share appreciation alone has paled in importance to the power of its reinvested dividends. The results are similar for others like AmeriGas Partners (NYSE: APU) and Ferrellgas Partners (NYSE: FGP); reinvested dividends skew both companies' total returns dramatically higher. If you're a long-term shareholder, don't worry about daily share wobbles. Devote your attention to those dividend payouts and your commitment to reinvest them.

And how do Buckeye's dividends look? At 6.5%, its yield is over double the market average. The company has paid a dividend every year since 1987. Buckeye is set up as an MLP, so the tax structure can become tricky (read here for more). MLP's aren't for everyone, but their unique structure of emphasizing dividends (commonly referred to as distributions) provides one of the most effective ways to harness the power of compounded returns over time.

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.