There is no straightforward answer to the question how many credit cards are too many. The average American has three open credit cards. If you have so many that you can not manage to keep up with the monthly payments, due dates, interest rates, fees, charges, and other important information then this is too many.
Too many credit cards can cause you to have a higher debt to income ratio. Lenders contemplate your available credit and treat it as potential debt when they evaluate your loan applications. If they calculate assuming that all of your cards get maxed out, then this may cause your debt to income ratio to be treated as over 37 percent. This is a point where you might consider closing credit card accounts (newest ones first to not impact your average credit length history too much).
With more credit cards, you may be tempted to use them to excess. It is important to keep your total credit utilization to less than 30 percent and ideally under 10 percent (this component comprises 30 percent of your credit score). The simple way to minimize your credit utilization is to keep a smaller number of cards.
You might be better served to have other types of credit in lieu of more credit cards. Credit score algorithms consider the kinds of credit you have to ascertain how much experience you have with other types of credit. Credit mix comprises ten percent of your personal credit score.
In the end, you need to have no more than one to three credit cards to avoid getting yourself into trouble. Managing them all gets much harder as you have more than three.