There's a ton of scientific, economic and demographic data sites aggregated at http://www.data.gov/

Basically the only requirements are some time and a curious mind.

There's also a lot of free data analysis tools available from the scientific and OSS community also. You can use various CLI tools or tools like pandas or IPython to help clean and analyze data. If you have a community oriented and OSS site you may also be able to find free hosting for your projects.

Some of the projects the group I work with are delving into are: rainfall trends, credit union historical analysis, metropolitan demographic shifts, vocabulary skills and possibly some NASA image analysis. I also help people use various tools to understand data before committing to write applications that incorporate the data.