You can get a new sim for each country. This might be the cheapest option, because anytime you cross a border—if you previous carrier has a roaming agreement with a carrier in your new country—you pay very high roaming charges for voice and data.

I don’t know Blackberries that well—does it have wifi? If so, you could make calls using Skype credit (2 cents per minute) with Fring — I use that on my Nokia with wifi. I have a Boingo mobile account to increase coverage, but it’s not an “everywhere” solution. For that, getting a pre-paid sim when you arrive each country is probably better.

If you’ll have laptop, then of course you could use Skype with it instead (same wifi issues as noted above).

Otherwise… back in the olden days, like 2005-2006, we used to use these things called “calling cards.” You use them from a hotel house phone, or from a pay phone, to call a number, put in your card’s passcode, and dial the number that you need to reach. You can buy these and print your own from Onesuite.com, or buy a calling card from a kiosk when you arrive to Europe. Just be sure what you buy in Europe has local access numbers for the countries that you plan to visit.