First, make sure you have a GSM phone with a SIM card to get service worldwide. Second, make sure that the phone supports the "frequency bands" that are used outside your home country. Ask the store or check on the manufacturer's Web site. Third, check with your service provider to see if they have "roaming agreements" in the countries where you are going, so you can use the other network when traveling there.
Those three things are needed for you to make and receive calls anywhere in the world, and to be billed accurately for them. While you check the availability of roaming from your service provider, you might want to check the rates of the airtime minutes. They vary depending on the country and tend to be very high compared to your rates at home. See also, What are the advantages to having a SIM in my cell phone or PDA?