Funders Online  calls itself "Europe's Online Philanthropic Community." It's an online directory of independent funders and philanthropic organizations in Europe and is supported by the Orpheus Programme, which can be considered the European equivalent of the Foundation Center in the United States.
Funders Online (FO) is definitely Euro-centric. Most mentions of funding amounts are in Euros or national currencies (when they haven't been converted). The site directs its users to organizations and reference lists that are specifically European.
To search FO for organizations that support science- or research-related activities, users must go to their advanced search page , not the simple search that appears on the FO home page. Under the search field "Subject Interest Area," scientists will find that the options "education," "environment," "health," and "science" apply most readily.
A search under "science" led to 56 search results for organizations that had registered themselves as supporting science (although they didn't indicate which scientific disciplines). A couple of U.S. organizations such as the Intel Foundation and the Rockefeller Foundation were included in the list; the rest were European. Search results under "health" included over 80 organizations.
Alas, most of these funders (who are independent and are not directly affiliated with any Eurogovernment agency) don't directly support scientific research. But if you're looking for funding to examine epidemiological outcomes or health policy or to set up long-term regional health studies, you may be in luck. Science education also appears to have some candidate funding organizations in this database.
The "Guide to Funding Research" provided by FO is not, as we first supposed, a guide to how to get funding for research. Instead, it's a guide on what types of background research a potential grant applicant needs to conduct on a funding organization's interests before applying for a grant. Despite our initial disappointment, we found the guide to be useful, especially for scientists who might be applying to a funding organization not usually known for its scientific or research activities.
The site offers nice navigation, helpful links to other lists of funders, and a useful news page on (relatively) recent funding changes or events in Europe. If you're searching for funding from organizations other than the usual suspects, it's worth a try to start here.
And we'd be remiss if we didn't point out that out sister site GrantsNet  has over 500 detailed program listings on biomedical funding programs, many of them open to non-US citizens!