Use your own number on local rates when traveling with Roamer app for Android and iOS
The only thing you need to do is activate roaming credits from the app in installments of $13, $16, $39 and $65, then get a local SIM from any kiosk when you land. Data is only needed briefly when you activate the card with Roamer and when you initiate the call, and these will be local mobile data rates applied, so nothing exorbitant.
The savings are enormous, but above all the call ID is your own motherland number, so you don't have to let everyone know your local cell, or have people wondering who's calling from Europe in this ungodly hour. App versions for BlackBerry and Windows Phone are in the works, too.