Jeez 3 years ago I had 1.
Now I have 7 Unless I'm forgetting one.
I feel like there is a maximum number. I just don't know what it is Minimum I would say would be 1 Visa or MC, 1 Discover or AMEX and 1 store card.
 I knew I was forgetting one! Make that 8!
I wouldn't worry about a maximum for a good score. My reports with 26 CC accounts showed 780-795 FICO. I closed two Amex accounts that were reporting from 1982 when I refused to pay a yearly fee. A few other accounts changed. I now have 22 CC accounts that show on my reports, 3 of which show closed. My FICO stays in mid 700s unless I have too many accounts with balances like now - 14 with balances giving me 709. I would never try to keep track of that many for personal use - I have three small businesses. The only one that reports that is not a normal CC is Kohl's.