Travel cheques are no longer the best way to carry your money while traveling. The places you can use them or change for cash are quite limited. Not even all banks will change them for you anymore...

Interesting question: In all the years I've been travelling around the world, I've discovered that one of the easiest way to access your cash (in the last 10 years) is with a bank card. Not every bank card will do.
The bank machine applicable has to be accessible everywhere, and not charge an exorbitant service fee.
It has to belong to banking system that is recognized world wide.
I used to have a card for my home bank in Canada ... but there were places it would work.
My wife suggested I try the bank she retired from, so I did.
It fills the bill perfectly.
Get an HSBC bank card and credit card. They are useable everywhere, they have branches everywhere, and their service fee is commensurate with what other banks charge. I used to use them in London all the time because if you use their ATM, there is no service fee. We are in Buenos Aires at the moment, and Benelco is the ATM of choice. But when we're in the downtown area, the HSBC is the only choice for financial transactions.
By the way, Japan is the odd man out. At last visit there were two places where you could actually use your bank cards. There is an ATM on the arrivals level of the NRT airport, and another under the stairs on the departures level. All the other in Japan only accept cards that are of Japanese origin. Go figure.

Mike Sr. gave a good answer. Basically, you are giving the issuer an interest-free loan since you've given your US dollars for the travellers checks. American Express offices (if you can find one) has low exchange reates if you are cashing in your travellers checks, but as Mike pointed out, you should stick with the bank/debit card of a bank that allow you a certain number of transactions at no cost or they rebate transaction fees. Whatever you do, do not go to your local bank to buy $100 of the needed currency or change money at an airport kiosk. It will probably cost you at least $20. A reasonable approach is to change a small amount of money at your hotel. It will cost you, but then you can look for an ATM machine. Know what ATM companies your bank has a relationship with. I recommend Navy FCU if you can join.

Mike Sr. and David hit all the points.Travelers cheques have become dinosaurs.Plastic is the way to go.As a military veteran...get an account with one of the FCU's they use.Rates are better and conversions are transacted easier due to the members travel so much. Your piece of paradise awaits your discovery...lets travel today! (http://pieceofparadise.agentarc.net )

To be on the safe side I like travelers checks.Bank cards are not good every where.Plus travelers check you can get reimburse if something go wrong.

Credit cards are safe too you get remiburse .