I once heard someone say you should have a credit card from each of the major processing companies: Visa, MasterCard, American Express, and Discover. That's definitely not the way to organize your credit card holdings.
Still, some people have their preferred credit card processor. Some prefer Visa and MasterCard because they're more widely accepted. Others like American Express because of the prestige. Which credit card(s) do you carry?
Note that there's a difference between the payment processing network - Visa, MasterCard - and the credit card issuer. Credit card issuers are the banks who issue the credit card, e.g. Bank of America, Capital One, etc. To make things even more confusing - Discover and American Express are both the credit card issuer and the payment processing network. This tutorial on how credit card transactions work may make it clearer.