There's a lot to like about dividend-paying stocks. Among other things, they provide you with real cash returns that give you the choice of what to do with a slice of the company's profits, and offer an inflation hedge when payouts increase. Additionally, dividend-paying firms make less cash available for executives to "empire build" or take on value-destroying projects, which can actually improve long-term profit growth.

On the other hand, over the past two years, we've seen the worst side of dividends -- cuts, eliminations, and suspensions. In the S&P 500, 62 companies cut their dividends in 2008, followed by another 90 in 2009, including Bank of America (NYSE: BAC) and Morgan Stanley (NYSE: MS). In 2009 alone, companies eliminated $58 billion in dividend payments to shareholders. Following regulators' warning to U.S. banks in March that dividends and buybacks shouldn't be reinstated until the economy has regained its footing, I wouldn't hold my breath for a recovery of their pre-crash dividend yields anytime soon.

Suffice it to say many dividend-based strategies have been turned upside-down, including one of my own.

Fool me once...
No one wants to get fooled (lower case "f") again, of course, but trading in and out of dividend-paying stocks doesn't make much sense, either. Instead, here are five scenarios where a long-term, income-minded investor should consider selling a dividend stock.

1. The dividend is cut or suspended
This is the most obvious reason to sell. Even if a cut is good for the business long-term, it could take years, if ever, before the dividend returns to its pre-cut levels. Consider the case of Pfizer (NYSE: PFE), which cut its dividend in half in part to help pay for its acquisition of Wyeth. True, the quarterly dividend was recently raised from $0.16 to $0.18, but that's still a far cry from the pre-cut level of $0.32. With analysts expecting roughly 2% annualized long-term earnings growth for Pfizer, it will likely be a long time before Pfizer pays $0.32 a share again. The downside to selling after a dividend cut is that you're often selling at depressed prices. Before you decide to sell, make sure you have a better place to move your funds.

2. The company can't afford its debt
Common stock owners rank lower than creditors on the totem pole. If the company doesn't generate enough profits to cover its interest payments, it's time to get suspicious of the dividend. According to Capital IQ, 88 U.S.-based dividend-paying firms had market caps greater than $1 billion and interest coverage ratios (EBIT/interest expenses) below 2 in January 2008; 41 of them have since cut their dividend.  

3. Free cash flow dries up
Dividends are only sustainable if the firm generates more than enough free cash flow to cover the payouts. In 2007, International Paper (NYSE: IP) generated roughly $770 million in free cash flow, which more than covered its $436 million dividend. In 2008, International Paper bought some of Weyerhaeuser's operations for $6 billion, raising concerns among analysts about how the company planned on paying for it. Unsurprisingly, the company cut its dividend by 90% a year later to help pay down that debt.

4. You no longer understand the business
A company you bought way back when may not be the same company it is today. If you no longer understand what makes it tick, it's best to get out. An October 2008 article in the Wall Street Journal highlighted an unfortunate case of an elderly investor whose retirement plan was crushed by Wachovia's dividend cut. Her husband had purchased shares of their hometown bank years earlier; it was subsequently acquired by Wachovia. Understanding the ins and outs of a local community bank is one thing, but a multiregional financial conglomerate rife with exotic mortgages is something else. A number of Wall Street analysts didn't fully understand Wachovia, either -- Merrill Lynch upgraded the shares in July 2008, just three months before it was forced by the FDIC to sell to Wells Fargo.

5. There's a better alternative
It's very easy to get emotionally tied to stocks that have paid you back year after year, but in some cases, you could do even better with other stocks. To illustrate, if you bought $10,000 worth of Deere (NYSE: DE) in May 1990, your investment is now worth about $41,000, and you're raking in roughly $813 a year in dividends. Not bad at all. 

However, Deere's current dividend yield is just 1.9%, and there are plenty of fine dividend stocks yielding more than 3% today, such as Coca-Cola (NYSE: KO) and McDonald's (NYSE: MCD). If your objective is income generation, you could consider selling your Deere shares and rolling the proceeds into a quality stock paying 3%, thus increasing your annual dividend income to $1,230. Alternatively, if you sold half your Deere stake to diversify, your new annual income would be $1,022. As always, be mindful of tax implications when selling stocks for a considerable gain.

It's strictly business
Despite the myriad benefits of dividend-paying stocks, at the end of the day, they're still stocks. As such you need to periodically review them to ensure they're the best place for your money. Dividends, after all, are a privilege, not a right. As the events of the past two years have reminded us, they're not reason enough to hang onto a stock.

Having a set of reasons to sell a dividend stock, then, is just as important as having a set of reasons to buy. It helps you become a more disciplined investor, even if your favorite holding period is forever.

If you'd like to learn more about dividend investing, Motley Fool Income Investor can help. Advisor James Early and his team have assembled a group of stocks with an average yield of 4.2%, and they provide valuations and risk ratings for each recommendation. You can start your free 30-day trial to Income Investor by clicking here.

Fool analyst Todd Wenning is hoping the Cincinnati Reds can go at least .500 this year. He does not own shares of any company mentioned. Coca-Cola and Pfizer are Motley Fool Inside Value selections. Coca-Cola is a Motley Fool Income Investor recommendation. The Fool's disclosure policy is never a sell.