If your GSM BlackBerry (e.g. one from AT&T or T-Mobile) supports the 900 and 1800 bands, you can use it in many countries outside of the United States, especially in Europe.
And, if you turn your phone on for the first time while abroad but it appears that no coverage is available, your phone may be defaulting to the GSM bands that are only used in the U.S. 850 and 1900.
To change the default, open the Settings menu and then manually scan for available networks. Once you find a frequency that works, select it and you should be good to go.
(Bear in mind that international roaming charges can be extreme—in some cases up to several dollars—so be sure to check your plan before you leave the country.)