Well, I do population genetics, but there are databases which you can get access to phenotype data for free. For instance, ARIC (atherosclerosis risk in communities) (
http://www.cscc.unc.edu/aric/) is a population based cohort of individuals followed since 1987. There is some great stroke and carotid disease data in there.
The problem with these free datasets is that they are usually beaten to death. ARIC has over 700 publications on it. You can get access and play with the database, but chances are you are not going to find something new. Now, if you just want to do this for a school project or something, that might be fine. Longitudinal epi studies are expensive, and the investigators get a 12 month protected window after each stage of the project before they have to publicly release the data. This puts you at a disadvantage if you aren't part of the study.
Of course, the grand-daddy of them all, the Framingham Heart Study (
http://www.framinghamheartstudy.org/), is also free, although you need to petition their review board and present a project proposal for access.
If you're interested in imaging and/or genetics and don't care that it's a case-control cohort, the ADNI project (
http://www.loni.ucla.edu/ADNI/) has extensive phenotype information on probable AD and MCI cases and cognitively normal controls. Even if you don't have access to a high-performace computer cluster to do imaging or genetic analysis, you could play around with the phenotypes alone. Again, there probably isn't much new to find in there, but I'm not sure what your goal is, so that might be fine.
These are just examples that I have experience with. There are plenty more out there.
