Just because an account is closed, doesn't mean it doesn't have an impact on your credit rating for a certain number of years.
Not sure about the US, but in Canada things stay on your credit report for 6 years or more depending on what it is. A first time bankruptcy will be there for 6 years. Subsequent ones longer.
Also, creditors take into account your debt-credit ratio. Which means that as you pay off credit cards and close them, your debt-credit ratio actually increases which can end up affecting your credit in a negative way. Department store credit cards like Sears etc are not as bad to close after they are paid off, but it's actually better to keep your cards like Visa, MC etc open without using them, until they are all paid off.
For example... let's say you have 5 bank credit cards. One has a credit limit of $15,000 which is maxed out. One has a credit limit of $10,000, and the other 3 have credit limits of $5,000 each. That's a combined total of $40,000 credit. If out of all of those cards you owe $15,000 your debt-credit ratio is based on the $15,000 debt and the $40,000 credit which you have. That is looked at as favourable... you have $25,000 free credit available.
Now on the other hand let's say that you have been closing each card as you pay it off and are now left with only one credit card .. the one that is maxed out at $15,000. Creditors look at you as a high risk. You have $15,000 debt, but you also only have $15,000 credit which means you have zero available credit... so you appear to them as a high risk regardless of having paid off the other debts.
Probably more information than what you were wanting, but since I declared bankruptcy I have been doing a great deal of reading on money management and it's quite the eye opener!