Banco Progresso wouldn't cash my travelers cheques without one and even most of the exchange houses want to see a passport when cashing travelers cheques. It makes things easier if you have one.
You don't need one...(it's not manadatory) my kids(too young to have id's) don't have one they are American citizens and they just get the back of their birth certificates stamped....of course having one makes it whole lot easier....
I don't think you need one to enter the country, but you may need one to exit the country you are travelling from. You don't say where you are, but certainly here in England you can't travel abroad without one.