Fortune scoured the globe for cities that share the San Francisco Bay Area's potent combination of creativity and capitalism. We started with data from the Global Innovation Index (co-published by Insead and the UN's World Intellectual Property Organization), which ranks countries based on a number of factors, including educational institutions and digital infrastructure. Crucially, the index also looks at results -- it essentially assigns extra credit to countries whose companies and institutions push their products and ideas out into the world.

We then looked closely at the cities and communities within the top countries that were leading the charge on innovation -- the places that are especially hospitable to companies seeking the mix of talent, curiosity, and risk taking that leads to game-changing new products and services. Northern European countries (some perhaps reaping the benefits of being outside the eurozone) dominated the list. If these cities keep churning out results, soon we won't be asking, "Where's the next Silicon Valley?" Instead the question on everyone's lips may be: "Where's the next Copenhagen?"

Zurich

Switzerland

When Google looked to set up its European engineering headquarters, it turned to Zurich, and Yahoo followed suit. The U.S. tech giants liked Zurich's robust broadband infrastructure, but the real appeal is the local talent: Switzerland is the No. 1 country in the world in patents as a percentage of GDP. The Swiss government has multiple programs for investing in small businesses, and the effort seems to be paying off. Zurich is home to hundreds of startups, including calendar software maker Doodle and Wuala, a cloud storage company.

Good for

• R&D/inventions
• Hardware
• Green/sustainable

Stockholm

Sweden

Stockholm has already produced Spotify and SoundCloud, and with nearly 700 high-tech companies located in its Kista neighborhood (Sweden's "Wireless Valley") the world can expect more tech innovations. The government spends on R&D (3.6% of GDP), and the country's world-class education system churns out a large pool of scientific publications and research. Intel, Symantec, and Oracle all have local offices, but lest you think Stockholm is studious and serious, please note that Angry Birds maker Rovio just opened a studio there.

Good for

• Software
• R&D/inventions
• Business-friendly policies

Singapore

Singapore has its sights set on becoming a hub for health technology, and the city-state has developed a package of incentives to lure large employers and upstarts alike. The program includes tax credits for R&D spending, plus access to Singapore's cutting-edge telecom infrastructure and scientific talent graduating from the country's highly ranked engineering programs. The inducements seem to be working: In recent years pharmaceutical giants GlaxoSmithKline, Novartis, Abbott, and Roche have opened major operations in Singapore.

Good for

• Science
• Education
• Business-friendly policies

Dublin

Ireland

Dublin is cheaper than London, boasts low corporate tax rates, and everybody speaks English. Its "Silicon Docks" neighborhood houses tech giants Google, Facebook, LinkedIn, and Zynga. Last year Twitter announced that it was opening its third international office (after London and Tokyo) in Dublin, making the city its European headquarters. The annual Dublin Web Summit is one of the fastest-growing tech conferences in Europe.

Good for

• Education
• Hardware
• Business-friendly policies

Copenhagen

Denmark

Last year a group of tech executives created the Founder's House in Copenhagen, an invitation-only workspace designed to incubate upcoming tech entrepreneurs. It's located a few miles from Nokia's local campus and hosts tech firms like Ge.tt, an online storage outfit, and app-hosting platform AppHarbor. The companies also receive help from Denmark's talented developers (C++ and Ruby on Rails were developed by Danes) and business-friendly regulatory environment.

Good for

• Mobile
• Business-friendly policies
• Science

Oulu

Finland

The remote city of Oulu, about 300 miles north of Helsinki, has a population of 140,000, and 18,000 of them work for the more than 800 high-tech companies that operate here. These include branch offices of Nokia, Indian tech giant Wipro, and Pulse, the U.S.-based news-reading app. Local officials work closely with the University of Oulu and businesses to foster innovation through programs like Xpolis, which connects investors to local startups.

Good for

• Mobile
• R&D/inventions
• Business-friendly policies

Eindhoven

The Netherlands

The Intelligent Community Forum, a nonprofit think tank, ranked Eindhoven's tech neighborhood (dubbed Brainport) the world's smartest region in 2011. The one-square-kilometer area is home to more than 100 companies and institutes and some 8,000 researchers, developers, and entrepreneurs who churn out nearly 50% of all Dutch patent applications.

Good for

• Green/sustainable
• Software
• Online participation