The Cingular Treo 650 is actually a Quad-Band phone which means it works on every conceivable GSM network around the world. GSM is used throughout Europe and the Middle East as well as in many parts of Asia and in Australia. Check that the country to which you are traveling has GSM to be sure. (South Korea for example does not.)
As the previous poster suggests, you need to make sure the phone is unlocked in order to be sure that it will take foreign (non-Cingular) SIM cards - this means it will also work with T-MObile in the US..
Anyway, Cingular is pretty nice about unlocking phones as long as you are a customer in good standing. They will do this for you even if you are a "Go Phone" customer. That means that even if you are on a $29.99 plan that is monyhj-to-month they will provide you with unlock code for your phone provided you give them a good reason - like you will be overseas for a few weeks.
The problem is that their unlock codes do not always work. Even if its the correct code etc. I had this problem recently. When I researched online I found that something has changed and their unlock codes SAY that your Treo 650 phone is Unlocked, but it is not. Long story short - there are unlocking companies online who will unlock for you for about $20. I won't mention any names and I advise you to check any legal issues before taking this advice.
Once unlocked with the correct code your Treo 650 will work perfectly with other carriers. Save the unlock code. Certain upgrades in the future could relock your phone so you want the code so you can punch it in again should the need arise.
If you have a Treo 600 phone - these unlock readily with a code. You can also find a patched firmware which when installed does not require you to enter any unlock code.
I hope this helps!