BARCELONA—For Google Inc., Europe's economic turmoil has had a silver lining: Smartphones that use the Internet giant's software are crushing the iPhone in countries hard hit by the continent's debt crisis.

Last year, despite Apple Inc.'s high-profile launch of the new iPhone 4S, only 5% of the smartphones sold in Greece and 9% of those sold in Portugal were iPhones, according to research firm IDC. Most of the rest were phones running Google's Android operating system, which the company is promoting heavily as it seeks a...