How many credit cards should you travel with?

I encountered a minor nuisance while at Delhi airport on my way back from a quick trip to India: the Wi-Fi network you have to pay for. I stumped up for the connectivity, but a colleague had less luck — not because he wasn’t willing to pay, but because the service in question would only accept Visa, and not MasterCard.
When I first began travelling the world, it was accepted wisdom that you needed both Visa and MasterCard to be sure of credit cards being accepted, with the former predominant in Europe and the latter a necessity for the US. These days, I find that pretty much anywhere that takes credit cards accepts both — but as the Wi-Fi example shows, the experience isn’t universal. Having a backup card certainly avoids that kind of problem, and also gives you an emergency option if one card is damaged or stolen (especially if you don’t store them together).
But is that a sensible strategy? Is carrying two cards just in case one doesn’t work fiscal prudence gone mad? What other strategies do you use to avoid being caught out when it comes to paying for goods on the road? Share your thoughts in the comments.