Before choosing which route you want to go, you must first know how many countries you are traveling to and how you will keep in contact with family and friends at home as well as people you meet while abroad. There are many different approaches to take regarding a mobile phone when traveling abroad.
First step is to make sure you have an International Phone and to ensure that the phone is unlocked for international usage. I would not recommend using your home data plan unless you are willing to spend an unnecessary amount of money to make calls.
For starters, Europe differs from the US because most places have Wi-Fi where as in the US most people use data plans. European airports, train stations, accommodations, and restaurants usually offer free Wi-Fi. You can use this free Wi-Fi to call or text family and friends for free. For more information on how to text and call for free, please see my Useful Apps page!
Single SIM Card : The single SIM card route can work very well if you are backpacking multiple countries for a short amount of time. I purchased an Ekit card which gave me fantastic call back rates to the US and Australia while traveling throughout Europe. This plan also allowed me to purchase a data plan which I used for emergencies. I was also able to receive free incoming calls and text messages, in which case I would return the call or message once I found a Wi-Fi zone.
Multiple SIM Cards : SIM cards can be purchased in each country for the most favorable rates. This can be a great way to go about using your mobile phone cheaply, but I would only recommend this if you are hitting a select few countries. If you are only spending a few days in each country, you will end up losing money on the plans you don't fully use and also spend a decent amount of time shopping around for a new card each time you travel.
Purchasing A New Plan : Many people that travel may have a "home base" in which they'll spend the majority of their time in that one country. If you're traveling to the US or Australia, I would recommend purchasing a plan since you'll get all the perks without roaming fee's. If you are in Europe, it may be that you'll be at home during the week and traveling on the weekends. In this case it would make sense to go the route of a company such as Vodafone that will work throughout all the countries with minimal roaming fee's. If you purchase the plan in your home country you'll only pay roaming fee's once you leave the country on the weekends, in which case you can still use the free Wi-Fi provided and pay for the minimal usage when not in those zones.