Generally, if you carry balances on your credit cards, canceling one of the accounts will hurt your FICO score.  One key factor in the FICO calculation is the debt utilization ratio, which shows how much of your available credit you are actually using.  If the total of the limits on all your cards adds up to $20,000, and your balances add up to $10,000, you have a utilization of 50%.  That doesn't sound too bad, right?  Actually, that is relatively high in the eyes of the FICO calculation.  You should try to keep utilization low, below 30% if possible.  Zero percent utilization is best, of course, because creditors love most to loan money to people who appear not to really need it!

Keeping the credit utilization discussion in mind, its easy to see how canceling a card account can lower your FICO score.  Lets say you have that same $20,000 cumulative limit, and you close an account with a $5,000 limit.  That same $10,000 balance nets you a 66.7% utilization, quite a bit higher than the 50% it would otherwise be.  The higher utilization lowers your FICO score.

 A similar thing happens when a card company lowers your credit limit.  This has angered consumers across the nation.  While banks reign in credit exposure, consumers are hurt by the utilization calculation.

But, how much will your FICO score suffer from closing an account?  This question was answered recently on the SavingAdvice forum by frequent poster Boosami:

 In general, it's easiest to keep them open to be sure your FICO won't be affected. However, if it annoys you to keep them open, here's instructions to figure out if it will affect you.

1) Determine your total balance reported to the credit bureaus for revolving accounts. Credit cards, unsecured loans only.
2) Determine your total available limit on all those tradelines from above.
3) Calculate your overall utilization percentage (#1 divided by #2).
4) Determine your new total available limit, ignoring the cards you wish to close.
5) Calculate your new overall utilization percentage (#1 divided by #4).

Compare your current and new percentages. The new one will be higher. If it's less than 10% higher than the previous, cancelling those cards will not significantly impact your FICO. The higher the percentage is, the more it potentially reduces your score.

Thanks to Boosami for providing guidance on how account closure affects the FICO score.  As he describes, when deciding whether to close an account, you should be cautious if your utilization changes by 10% or more.  In our example above, utilization changing from 50% to 66.7% is significant, and would have a noticeable impact on the FICO score.  If you are in a situation where you might need credit in the future, to finance a car, refinance a mortgage, etc, you probably would not want to take this action.  It makes more sense to keep the account open, active, and in good standing, until after you obtain the loan you seek.