Publicly Available Datasets
There is, in fact, a very reasonable list of publicly-available datasets, supported by different enterprises/sources. 

Some of them are below:


Public Datasets on Amazon WebServices;
Frequent Itemset Mining Implementation Repository;
UCI Machine Learning Repository;
KDnuggets -- a big list of lots of public repositories.


Now, two considerations on your question. First one, regarding policies of database sharing. From personal experience, there are some databases that can't be made publicly available, either for involving privacy restraints (as for some social network information) or for concerning government information (like health system databases).

Another point concerns the usage/application of the dataset. Although some bases can be reprocessed to suit the needs of the application, it would be great to have some nice organization of the datasets by purpose. The taxonomy should involve social graph analysis, itemset mining, classification, and lots of other research areas there may be.