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Yes, most of Europe will take your visa card, but not everywhere.
Visa is one of the best accepted ones, the other is Mastercard, but there are still many places that do not accept cards at all, or only for a fee.

So you should have some cash. The cheapest option is to get it out of the ATM with your bank card, as your credit card will almost always treat it as a cash advance and charge you a lot of money for it.
If you have an American credit card and bank, you should inform them that you will be using your cards in Europe, in most other countries it is good to do so, but not as needed.
By calling them you can assure yourself that your card is ready for use in Europe.

A little cash taken from home can be good, but traveling with just cash you run a high risk of loosing it too pickpockets or because you are not careful enough with it.
And if your wallet is full of money, you are more likely to overspend. Which is also a risk if you put everything on your credit card.
Source(s):
I travel often, in Europe and farther from home.