Did you search? This has been discussed ad nauseam. A simple search, for example, for "international cheap cell mobile" on this forum returned 47 threads.
You can pay for Verizon/AT&T/whomever. Or you can forward your US cellphone number to a Skype account before you leave, and get a prepaid SIM in each country. When you get a new SIM, you set your Skype account to forward to your new SIM's number. Keep your Skype account balance topped up and you'll be in business.