Some countries insist that you show some means of support (credit cards or cash), or have evidence of an address where you will be staying (hotel, friends, etc.) while visiting. You may also need to show return or onward air tickets.
This is mainly to show that you don’t intend to stay for an extended time in the country (illegally), and you won’t become a burden to the state (and won’t need to be flown home at their expense, for example).
This is known as the ‘sufficent funds’ requirement. New Zealand, for example, requires that you have about $15 per day of intended stay. Canada will turn you away if you can’t show you have ‘enough’ money.
Any credit card (regardless if it has a low limit or is ‘maxed out’) should be OK to show you have sufficient funds at most borders.
It helps if you look OK when crossing the border, too, (i.e. not poor or dishevelled). Being clean shaven and wearing clean clothes just for this purpose is a good idea.
You can find more about taking money and credit cards with you in the ‘Money‘ section of this website.
