At first thought, I would think that canceling a credit card would improve your credit score because it would reduce your total available credit. But it doesn't quite work like that.
After some research and help from fellow bloggers, it all comes down to the length of time that you held the credit card. The older the credit card, the more weight or importance it has on your credit score. In other words, credit history is an important factor in the credit scoring system. Also note though that credit history only accounts for approximately 15% of your total credit score.
Here is what The Financial Blogger had to add:
It is true that it would hurt your credit score on a short term basis. However, if all your accounts are up-to-date, it will not make a huge difference after a few months.
The same situation happens when somebody is looking for financing for a mortgage or a car loan. That person might do 5 inquiries in the span of a month. It will automatically drop his credit score temporarily. However, after a few months, if he did not contract 5 loans but only one, his credit score will be back on track.
Within 6 months, closing a credit card will not have a significant impact on your credit score if you pay you other cards on time and if they are not maxed out. The key point with revolving credit is to have the outstanding balance fluctuate over time.
So to answer Canadian Dollars question, providing that the cards that you cancel are fairly new or newer than your other credit cards, your credit score should not be affected with any significance. However, canceling credit cards may be helpful if you're looking to get a mortgage in the near future as lenders look at the total credit available as one of their lending criteria.
Lesson learned: If you have an old credit card in good standing, then think twice before canceling it as it may negatively impact your credit score. However, as with any credit blemishes, time heals all credit wounds.
If you want to read more about how credit scores are determined there is tons of information on Thicken My Wallet and The Financial Blogger about credit scores.