There is no limit on the number of credit cards that you can have as long as the creditors are willing to approve your application. This does not mean however that it is a good idea to continually keep applying for credit. Apply for a number of credit cards that you feel you might need and not beyond. Two things are important with credit cards.
The total amount of credit available to you with all the credit cards combined and the amount of balance that you carry. Out of this the amount of balance that you carry is of a lot of importance. A high balance has compared to the credit limit is a sign of a higher credit risk.
While the credit scoring model considers low debt utilization ratio as favorable, a large amount of available revolving credit may deter certain lenders from extending you further credit.
This is especially true if your credit report reflects previous problems with meeting the payments on time. A lender will think that you can go ahead and charge of the unused credit accounts at any point of time and get yourself under more debt thus making repayment even more difficult.
So what you need to do is balance your debt utilization ratio with what the lenders might consider to be surplus revolving credit.
If you already have several credit on accounts open, you should consider getting a copy of your credit report and a credit score before applying for new credit cards or closing any of the credit card accounts. But using a credit score will provide you with detailed explanation of the factors that are influencing your credit score negatively and positively. You will be able to see clearly whether having surplus credit card accounts is damaging your credit score or not.
You must also make note of the fact that every time you apply for credit card and the lenders will probably make a request to see your credit report to the credit bureau. This request would be reported as an enquiry. Each subsequent lender that apply to receive this enquiry and will know that you have applied for credit elsewhere as well. Having too many enquiries for credit in a short amount of time can also affect your credit score as it is an indicator of financial trouble. Too many lenders it may mean that you are trying to incur a lot of debt which could be a potential problem in your application getting approved.