1. Studies have shown that, on average, the stocks sold by individual investors OUTPERFORM the stocks they subsequently purchased. That means that, statistically, the stock you just bought will do worse than the one you just sold. Consider some good businesses and the hard times they had in the 1990s: AOL's accounting troubles around 1996, Best Buy's supply chain and public relations disasters of 1996-97, Dell's early uncertain prospects for competing with the "big boys." Had you sold ALL of your stock in one of these companies when it had bad news, you'd have reason to feel awful. If, on the other hand, you kept even one-fifth of your original shares, you'd still have at least a double on your original investment, regardless of what you did with the four-fifths you sold off.
2. According to a recent article in Individual Investor magazine, men tend to forget their investing mistakes. By keeping a few shares of that Big Mistake in your portfolio, even as it slowly slides down to zero, you will relearn your lesson every day. It will serve as a reminder not to slip up again, and it may save you from making a much more costly mistake later. The great Warren Buffett has a willingness to remember (and repeatedly acknowledge) his mistakes. He has made many mistakes, but almost never the same one twice.
3. Holding on to a dog stock gives you a chance to learn an industry. As you follow the stock for years, or even decades, you will learn about the effects of competitors, suppliers, customers, inflation, energy prices, raw materials, strikes, manias, panics, foreign markets, etc., on the price of your stock. You will also learn how its price moves in relation to other stocks in your portfolio. In most cases, you'll see that the stock keeps plodding along despite all the turmoil. It's the kind of education you can best learn by observing for the long-term. You might even find that the stock you sold starts to turn its business around a few years later (maybe its unscrupulous CEO finally retired!). You now have a buying opportunity that you might have missed had you sold your shares.
Now, I'm not suggesting that you never sell a stock, but before you do, consider whether saving a small percentage might impart a lesson far more valuable than the few dollars the shares are worth today.