A little attention paid to dividends can really pay off. You may think of venerable blue-chip companies such as US Bancorp, General Mills, Merck, General Electric, and Citigroup as stodgy and old-fangled, but think again. They often pay generous dividends.

If you bought stock in a solid growing company when its dividend yield (annual dividend amount in dollars, divided by share price) was 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 it pays 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). Now, $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 in one 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 just 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.

With many great dividend-paying companies, by holding on, your dividend yield keeps rising. Consider this: One share of Coca-Cola, bought in the company's first year on the market, has become more than 97,860 shares through stock splits and dividend reinvestments. That investment is now earning an annual dividend of more than $114,000.

One way to take advantage of the power of dividends is through "Drips" (direct investing plans, or dividend reinvestment plans). Learn more in these articles:

Coca-Cola is a Motley Fool Inside Value pick. US Bancorp is an Income Investor pick, while Merck was a former selection of that newsletter.