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The ADNI project (2004–ongoing) aims at characterizing change in cognitive functions and brain structures with age, with a particular emphasis on Alzheimer's disease and neuroimaging.

From the website,

The overall goal of this huge project is to define the rate of progress of mild cognitive impairment and Alzheimer's disease, to develop improved methods for clinical trials in this area, and to provide a large database which will improve design of treatment trials. We expect that this project will provide information and methods which will help lead to effective treatments for Alzheimer’s disease, leading to effective prevention.

Data that are collected include: demographics, clinical data, neuroimaging (MRI/PET) data, and a wide range of cognitive tests. (More on ADCS website.) Details about protocols, available data can be found under ADNI Scientist's Home. In particular, data are available on ADCS. Please note that you must write an application to get the data (as is often the case).