CRISP (Computer Retrieval of Information on Scientific Projects) is a searchable database of all US federally funded biomedical research conducted at universities, hospitals, and other institutions. The database is maintained by the Office of Extramural Research at the National Institutes of Health. It is a vast resource covering projects for the past 30 years, and includes abstracts of what the researchers proposed. It also covers research carried out in New Zealand funded from the US. Searchable by disease, by country, by researcher, and more. A truly enormous resource.
Tips:
Searching PubMed for a year or two after the grant may get you the published results of the project.
Pubmed abstracts will also produce the names of key investigators, and may include details of the institutions they work in.

ClinicalTrials.gov is published by the U.S. National Institutes of Health to provide patients, family members and members of the public with current information about clinical research studies.

New Medicines in Development is a publication of The Pharmaceutical Research and Manufacturers of America (PhRMA) and lists 418 new biotechnology medicines in development for more than 100 diseases, at the time of publication in 2006.

The Europa website of the European Commission provides information on research in its Sixth Framework Programme.  One theme, life sciences and biotechnology, is particularly relevant. However there is limited information about projects funded.