My believe is that you should have at least one card from each of the 4 major credit card : VISA, Master, American Express, and Discovery.
Then you should have one VISA or Master from bank or credit union that is associated with your university or company or other organizations (for example, United Airline if you fly a lot), which usually will give your preferential treatment. Funny thing is that VISA and Master card is not necessarily accepted everwhere. For example, in Japan, some restaurants only accept Master card but not VISA (and you would expect the other way around).
Then maybe you can have some card for some special purpose. For example, American Express for COSTCO.
I would recommend that you should have around six (6) credit cards, and have total credit limit > $50,000 USD. This way, you can have a good credit score, as far as in terms of credit card category.
Assuming you pay off your credit card in full every month (and there is absolutly no reason you should not do so), I suggest that you choose credit card based on the following two criteria
- service, especially proteciton against fraud
- % of reward / rebate AND no annual fee
Personally I like Chase Sapphire Credit Card, because they have great service. For example, when I call customer service, I directly get a live person instead of the machine. Also, they have great fault detection program, and they have caught stealing usage within 30 min for me couple of times. The 1% rebate also helps.