When traveling abroad, you could try to use your carriers' international services for making calls or accessing the internet. However, those services can be costly and can definitely add up during your trip abroad. Also, your carriers' service internationally can just be plain terrible.
It's best to purchase a prepaid sim card with a local carrier in that country to use as their services are tailored to that country/location. Leo recommends going to http://prepaidwithdata.wikia.com/ to read the most up-to-date information on prepaid mobile phone plans around the world.