A little attention paid to dividends can really pay off. You may think of venerable blue-chip companies such as Ford (NYSE:F), General Mills (NYSE:GIS), Merck (NYSE:MRK), General Electric (NYSE:GE), and Citigroup (NYSE:C) as stodgy and old-fashioned, but think again. They often pay generous dividends. (Recently, Ford was offering 3.8%; General Mills, 2.8%; Merck, 4.9%; GE, 2.3%; and Citigroup, 4.0%.)

If you buy stock in a solid, growing company with a dividend yield (annual dividend amount in dollars, divided by share price) of 3.6%, you're very likely to get that 3.6% payout every year, regardless of what happens to the stock price. (Struggling companies may decrease or eliminate their dividends, but they try like heck not to because it looks really bad. Firms aim to maintain or increase their dividends over time.) Couple stock appreciation with dividends, and you've got an appealing combination.

Here's something investors rarely consider. Let's say you bought 10 shares of Stained Glass Windshield Co. (ticker: STAIN) for $100 each, and they pay a respectable 2.5% dividend. With a $1,000 investment, that amounts to an annual payout of $25. Not bad.

But wait -- remember that dividends aren't static and permanent. Companies tend to raise them over time. A few years down the line, perhaps STAIN is trading at $220 per share. If the yield is 3%, it's paying out $6.60 per share (0.03 times $220 equals $6.60). Note: $6.60 is a 3% yield for anyone buying the stock at $220, but since you bought it at $100, to you it's a 6.6% yield. You paid $100 for each share and each one is kicking out $6.60 to you.

Decades pass. Your initial 10 shares have split into 80 shares, each currently priced at $120. Your initial $1,000 investment is now valued at $9,600. The yield is still 3%, paying $3.60 per share ($3.60 divided by $120 equals 0.03, or 3%). Since you own 80 shares, you receive a whopping $288 per year. Think about this. You're earning $288 in dividends a year on a $1,000 investment. That's 29% per year (and growing) -- without even factoring in any stock-price appreciation. The yield for you has gone from 2.5% to 29% -- all because you hung on to those shares of a growing company. That's security! Even if the stock price drops, you're still likely to get that 29% payout.

Some folks will view this from a different perspective and will take issue with the 29% payout, pointing out that one should always look at the current dividend (3% in our example above) and see if it can be topped elsewhere. That's fair, but it's also true that if you've invested in a company that remains healthy and growing, you can do very, very well just hanging on and enjoying the dividends -- and ideally, reinvesting them!

With many great dividend-paying companies, by holding on, your dividend yield keeps rising. Consider this: One share of Coca-Cola bought in its first year has become more than 97,860 shares through stock splits and dividend reinvestments, and that investment is now earning an annual dividend of more than $58,000.

One way to take advantage of the power of dividends is through "Drips" (direct investing plans or dividend reinvestment plans). Read more about the power of Drip plans.

You're also invited to take a free trial of our Motley Fool Income Investor newsletter, which will permit you to peek at a long list of dividend payers recommended by Fool analyst Mathew Emmert.

Learn more in these articles that Mathew has written:

Merck is an Income Investor pick.