Biased reply (I'm a data scientist there): Common Crawl[1]. We build and maintain an open repository of web crawl data that can be accessed and analyzed by anyone completely free.

[1]: http://commoncrawl.org/

This thread is pretty good

http://www.quora.com/Where-can-I-find-large-datasets-open-to...

The Cancer Genome Atlas, Ensembl, 1000Genomes.