The Common Crawl is a project that has been crawling the web and making an open corpus of web data from the last 7 years available for research. There crawl corpus is petabytes of data and available as WARCs (Web Archives.) For example, their 2013 dataset is 102TB and has around 2 billion web pages. Their collection is not as complete as the Internet Archive, which goes back much further, but it is available in large datasets for research.