This article is from the Credit cards and Consumer Credit FAQ, by firstname.lastname@example.org (Steve Adams) with numerous contributions by others.
In the U.S., almost any establishment that takes MasterCard takes
Visa, and vice versa. If you're going to be doing all your spending
in the U.S., you may not want or need both cards.
In Europe, things are a bit different. In some countries, the Visa
and MasterCard networks have been merged, and ALL merchants who take
one take the other. This is notably the case in France. (But sometimes
the merchant isn't aware of this until you point out the M-C logo on
his sticker in the window.) On the other hand, the cash advance networks
have NOT been merged. Again, in France, almost any bank or cash machine
(if you have a 4-digit PIN) can give you a cash advance on Visa (Carte
Bleue), but only a few banks (Credit Agricole, Credit Mutuel, and all
Post Offices) and cash machines can give you a M-C cash advance. Also,
for various reasons, a given card may not work on the day you most need
it. And in many countries (e.g. Italy), the networks have not merged.
Thus, it is most prudent to have both.
American Express, Diners Club, and their kin were originally aimed
at the more upscale "travel and entertainment" market. They are
accepted at many places, though not as many as Visa and MC. Some
places don't take MC and Visa but do take American Express or DC.
In Europe, there are vanishingly few places that take only DC. There
are a very few that take only AE.
Note that credit card usage and acceptance varies widely across
Europe. In France, you can use it at MORE places than in the US. In
Italy, less in general, except for tourist-oriented shops. In Germany
and England, about the same. In Greece, only in tourist-oriented
The American Express card used to be very handy for travelling in
Europe. Among other things, it would let you cash personal checks
drawn on your U.S. bank at any of their many offices. Nowadays,
however, with your Visa or Mastercard, you can get cash advances at
local banks, at a better exchange rate.
Amex also holds mail for their customers at their offices; so if you
don't know where you'll be staying in Istanbul, you can have mail sent
to the Amex office. But it's enough to have one $10 Amex traveller's
check to be considered as a "customer".
I don't have an AmEx card, but someone who does posted a list of the
benefits he had actually used in a year and concluded that the card
was worth more money to him than the annual fee. He cited student
and non-student discounts for air travel, extra frequent-flyer miles
for a variety of airlines, and "twofers" at some big-city
restaurants. Your benefit will be different if your charging
patterns are different.
The best card for you is the one that is accepted where you shop and
charges you the least amount of money for the services you actually
use. (For example, if you always pay off your balance each month,
you want to make sure you get a card with a grace period but the
interest rate doesn't matter much.)