If you have any late payments, charge-offs or overspending associated with your credit card accounts, closing an account won't correct anything.
This is because the account history is in your credit report for at least seven years. You simply can't change your past.
Don't worry though, most negative items in your credit report will become less important with time. However, by canceling a credit card account, your good history might disappear as well.
Another reason why it's a bad idea to close old accounts that have no negative history, is that you would still benefit from them by having a long credit history. The length of time you have been borrowing is very important, since it can make up to 15% of your credit score. Entries that are good could stay in your credit report for a long time or forever.
Closing down credit card accounts could affect your debt-to-credit-limit ratio (which is the money you owe in credit card expenses divided by your total credit limit). For example, if you have one credit card with a $4000 credit limit and you spend $2000 on your credit card, your debt-to-credit-limit ratio would be 50% (2000/4000) but if you had another credit card with a $4000 credit limit, your debt-to-credit-limit ratio would be 25% (2000/8000). The lower the percentage, the better it is for your credit score.
If, for some reason, you find it completely necessary to close down one of your credit card accounts, you should close down one that doesn't have much history since it is always good to keep the ones with the most history because they are better for your credit score.
Make sure you don't just cut the credit cards, since that won't close your account. To properly close your account, call the number on your credit card statement or on the back of your credit card, speak to a real person and tell them you want to close the account "at the cardholder's request." It will appear much better on your credit report if the account was closed by you and not the bank.
Leave 'em alone
Contrary to the common belief that closing down a credit card account is a good idea, it can actually be harmful to your credit score and thus not such a good idea after all.
Closing down an account won't get rid of a bad history if you have one; it will affect your debt-to-credit-limit ratio and affect your credit score negatively. Also, don't close an account just because you think you have too many credit cards. Here's an article on how many cards you should have.
Closing down an account with a good history is not a smart move as that will no longer have a positive impact on your credit score. Also if you have to close down a credit card account for some reason, make sure to close down an account that doesn't have much history on it.