Minimum 3. Can't hit less than half cards reporting balances with 2 unfortunately, and that's a FICO penalty as we understand it.
Max, hard to say but people have been fine up nearish 20. There's anecdotal rumors of 25-30 being too many, and frankly from a rewards standpoint that seems absurd anyway.
Personally I'm going to wind up in the 7-10 range; I'm expecting 5-6 cards to actually be used for various rewards / features, a balance carrying card (or two) for financial defensibility purposes, and potentially a few pure tradeline farms for additional payment history (because my file is very short) and to make it easier to hit the needed less than 1/2 cards reporting balances without having to zealously manage my tradelines.
I want a higher credit limit (so more cards) a good balance of rewards cards, and to have a strong history with several lenders down the road. How many cards are too many? I should add that I always pay in full. Can too many cards ruin your chances of a 800+ score?
It only can if it's too many for you to handle and you miss a payment. If your util is low and you manage payments well, then it's no big deal. The right amount of cards is what's right for you and your DTI. Creditors will also eventually limit how much you can get since your exposure may be too high for income. You may reach a point where a denial comes because they think you have enough credit already.
For me. I don't want more than a few major cards and a few of my favorite store cards. I'm happy with that. I like rewards so I'm going to see what I can get to optimize rewards after we finish our house and close.