With stocks that pay dividends, investors may prefer the former strategy--you get income from both dividends on the underlying stock and from your calls. A problem that investors can run into with this strategy is that if their stock falls they may either have to write calls on lower strikes (taking a risk that the stock will be called from them for lower than they bought it) or sell longer term calls to get the same income.
Here's another way to get a decent income from dividend paying stocks that mitigates the above problem somewhat. Buy the dividend paying stock, and write a deep in the money LEAP call on it. While this severely limits any potential capital gains, it increases your dividend yield.
Here's an example. Let's say you decide to buy Pfizer (PFE) for its dividend (I don't think it's a very safe dividend, but let's say it is). As I'm writing, Pfizer is trading at $16.94 a share. The Jan '10 call at the 10 strike has a bid of $6.70 and an ask of $7.30. Let's say you're able to buy 100 shares at $16.94 and write a call for $7. Excluding commissions (these can vary, the cheapest I know of is $5 at Zecco), the net debit from your account would be $9.94 per share, or $994.
Pfizer's annualized dividend is $1.28 a share. Assume that the dividend payout will stay constant.
(A) Buying the shares without writing the call would get you a dividend yield of around 7.56%.
(B) Buying the shares and selling the call would get you a dividend yield of around 12.88%.
Scenario A leaves open unlimited capital gains, but offers downside protection of only $1.28 a share per year.
Scenario B limits capital gains to a theoretical $0.06 a share, or $6 in total (depending on broker commissions, the entire transaction will probably result in a slight loss--at Zecco it would be under $5). Pfizer can trade for $10,000 a share, but you'll only get $10 a share for it when the stock is called. Downside protection, however, is much better than in scenario A. As long as Pfizer trades above the price you paid ($9.94 per share plus commissions), you're not losing money, and this does not include the dividends you receive. While certainly riskier than a CD, the 12.88% dividend compensates for the risk rather well. As qualified dividends are charged a max of 15%, you may save on taxes here as well.
A danger with scenario B is that your shares may be called at any time. Here your gain/loss depends on how many dividend payments you have collected and what your commission costs are (update: as the commenter points out at the bottom, in most cases you don't get your annualized dividend all at once. In the case of Pfizer and most dividend paying stocks, dividends come once a quarter). The maximum you can lose if the stock is assigned is commission costs.
To mitigate the assignment risk and make the strategy in scenario B worthwhile, only do the deep in the money covered call write when the net debit from your account is less than the amount you will receive when/if the stock is called. While the Pfizer transaction above is an example, the $0.06 difference is not very much, and you will lose money on the enterprise if your shares are called too early (before your first dividend payment). A better example is Johnson & Johnson (JNJ). As I'm writing, JNJ is trading at $62.18 a share. The bid for the Jan '11 50 strike call is $14.80, and the ask is $16. Let's say you are able to buy the stock and sell the call, incurring a net debit of $47.39 per share. If the stock is called (which it will be if it's $50 or above when the call expires), you will receive $50 a share for it, giving you a capital gain of $2.61 a share (minus commissions).
As far as when to use this strategy, a bear market is the best time. As mentioned above, the traditional covered call strategy may run into problems when the underlying stock falls below your purchase price. During bear markets this possibility often comes true. This strategy is only worthwhile with dividend paying stocks. As with all stocks you buy, do your research. Don't use this strategy just because the spread between your net debit and the strike price is high (though this may be a good trade for gambling purposes).
Traditional covered call and LEAP "covered" call strategies work best in flat and slightly uptrending markets (if you don't mind getting assigned, raging bull markets work too). These strategies do not require dividend paying stocks to work.
To see this strategy in action, check out what I'm doing with Wells Fargo (WFC).
Disclosure: At the time of writing I owned JNJ.