Rule of thumb with credit cards is as few as possible. I highly suspect if you ran you FICO score, you already will be flagged for too many cards as I have seen FICO scored flagged for even less cards. It is easy to fix, by cancelling your cards down to 2.
The other important thing to do is not go over 50% of your credit limit on your cards. If you need more credit and have paid on time, most credit card company will up your limits. If you cancel you other cards, they also will up your credit limits because you have lowered you outstanding total credit.