Statistical Reference Datasets
itl.nist.gov
itl.nist.gov
While working on a library for deriving discrete maximum-entropy distributions recently, I had trouble coming up with good test cases. For that sort of thing, you either have to go flip through textbooks, search for other implementations (and hope they have a decent test suite), or think up problems to solve on pen and paper (which misses the sorts of problems you need numerical techniques to solve).
Even a collection of standard problems and datasets without canonical solutions would be valuable. Then everybody could start collecting results from different pieces of software to see which ones are anomalous. Does a website like that exist?
I believe that NIST is your best bet for finding reliable "Reference" datasets. In the distant past (i.e. around 2000), NIST made various "Special Databases" available. Some of them may be useful for the kinds of things you mentioned. The information on this FTP server is ancient and crufty, but might help in some way.
ftp://sequoyah.ncsl.nist.gov/pub/databases/catalog.txt
Also check the "README" files in the various directories. Though they are not the complete databases, there's some sample data available:
ftp://sequoyah.ncsl.nist.gov/pub/databases/data/
I simply don't know if NIST still has reference datasets like the old "Special Databases" that they used to provide, so I think your best bet is to contact them and ask.
Also Amazon (via AWS) [3] have made it really easy to access public data sets.
I hope this is helpful.
[1] http://archive.ics.uci.edu/ml/