Don't cut up that credit card yet...if you're going anywhere
You don't have to cut up your credit cards. You just have to use them responsibly, and never incur debt. Getting rid of them completely sounds good -- Bill W. had much the same advice for alcoholics about booze, and he was right -- but the action isn't likely to serve you well when you travel. A growing number of transportation sellers have gone cashless, so to travel without a credit card would cut you off.
With every passing month, more airlines announce they will only accept plastic on board. Last month, American Airlines declared its intention to offer in-flight purchases using cards only. Virgin America's food options can only be accessed by swiping the seat-back in front of you. JetBlue doesn't take cash, either, so if you want a blanket or some headphones and you only have greenbacks, you're out of luck.
Even trains are doing it. The new ACES between Atlantic City and New York City, which started last month, only does credit cards on board. (Amtrak still accepts cash.)
Rental cars have always been a particular problem. Forget about doing it with cash. Debit cards are problematic, too. Even if your rental goes off without a hitch, the length of time it takes for the deposit to re-appear on your account can really gum up your cash flow.
For those going abroad, having a card greases the process of getting foreign cash. If you bring cash and convert it into an international currency, you'll usually take a bigger hit in fees and poor rates. Here, I find a debit card is the best-case scenario; you set it up so it will draw from foreign machines. Credit cards usually incur fees from the first minute the money is withdrawn, so again, paying back right away (even if it means making a transfer via the web) is key.
The fact is that if you're going to travel, having a credit card makes life dramatically easier. Not having one could mean the difference between going hungry for six hours and feeling comfortable. You just have to make absolutely sure that your bill is paid in full every month and those expenditures don't mount.
Don't be mad at Suze. She's right about taking it easy with the credit cards, and even she acknowledges that in some cases, it would be smart to keep one of them around. Traveling is one of those cases.