I'm an American and have done most of my traveling starting from the US carrying US dollars. For the past few years I have been teaching English in South Korea, and in my first year here during my first solo trip I had the unpleasant experience of finding out that my Korean won are not all that desirable in some places. Changing won to baht was not a problem in Thailand, but when I needed to change money in Laos I had trouble finding a money exchanger who would take my won.
I know now that I should just use an ATM card to get money, but I am still wondering how can I know which countries will give me trouble with my won? And when should I change won to dollars before I travel?
You're not very specific so I will give a general answer
If you intend to bring lots of cash you have to check whether your destination country does lots of business with your currency. It doesn't surprise me that you had problems in Laos because Laos imports very little from Korea directly. Most imports go through a neighboring country so bills will be settled in those currencies rather than Won and thus the Won is little needed nor exchanged.
Cambodia does a lot of direct trade with Korea so you should be able to exchange in a bank. Vietnam does direct trade but the banking sector is controlled by the government so the exchange rate might not be favorable.
Indonesia and Malaysia shouldn't give you any problems. Myanmar I wouldn't try it.