Catherine,
This is a copy of the answer I sent to a couple of others, expanded with some notes about VISA / AMEX / etc acceptance:
I've worked in Rotterdam for the past 10 years, commuting from the UK most weekends, and there's a bit of truth in what all of you say.
In the UK (and everywhere else) we have two basic types of card - either a debit card or a credit card. With this type of card, money is held in a bank account and balanced against expenditure.
Generally speaking AMEX, VISA, Mastercard, etc., are widely accepted - but each shop will have a list of the cards they accept by the entrance.
The problem that Mike experienced is caused by the Dutch having a third type of card - a pre-payment card - which is a "Chip & Pin" type but which is not directly linked to a bank account.
You download money from your bank account onto the card - say Euro 200 - and you can then spend money off the card - until you need to recharge it with more money.
The Dutch like these cards because if you loose the card, the most you can possibly loose is the money you downloaded onto to it - there is no way that a thief can access your bank account from these cards.
Nearly everywhere - fuel stations, toll tunnels, hotels, camping shops, camp grounds, tourist shops, etc. take the standard European wide debit or credit card (and always take the pre-payment card) and you chip and pin like in the UK.
A few places ONLY take cash or the "pre-payment" card - most notably railway station ticket offices, parking meters in Rotterdam and Delft, and some supermarket chains like Albert Heijn. In this case you will need to take cash.
Robert