Before you leave home, check that your mobile phone can actually be used abroad. Most handsets sold nowadays are dual-band, which means they can be used throughout Britain and Europe, but if you're travelling to North America, you will need a tri-band handset, and places like Japan and Korea require a 3G-enabled handset.
Similarly, check with your mobile service provider that international roaming is enabled on your phone (this is the service that lets you use your mobile outside your home country). Most contract phones can be enabled for international roaming quite easily, if it's not set up automatically. On the other hand, some pay-as-you mobiles don't allow for international roaming, so it's always a good idea to check before you leave.
Also make sure you have a travel adaptor/charger that is suitable both for the voltage and outlet requirements at your destination, to prevent your mobile running out of charge and becoming a useless addition to your luggage.
(Image via al-hayat