The Memento Web and the Wayback Machine are two possible solutions:
Wayback Machine
The Wayback Machine by the Internet Archive is your best friend for all things that were once online, and even some things that still are, if you want to compare changes.
From Wikipedia:
The Wayback Machine is a digital archive of the World Wide Web and other information on the Internet created by the Internet Archive, a non-profit organization, based in San Francisco, California. It was set up by Brewster Kahle and Bruce Gilliat, and is maintained with content from Alexa Internet. The service enables users to see archived versions of web pages across time, which the Archive calls a "three dimensional index."
If you have a dead link, simply paste it into the search input element of Wayback Machine.
Alternatively, you can type https://web.archive.org/web/*/DEAD_LINK'S_URL directly into the address bar of your favorite browser.
Memento Web
Los Alamos National Lab has been offering the Memento Web project which unifies search across the archives.
Other
Some search engines may provide you with a cached version of the page where the dataset resided (possibly, the dataset files as well).
If the steps above fail, you may consider
- looking for papers which used the dataset (at arXiv or in academic journals),
- contacting their authors,
- looking at various bulletin boards for those who might have downloaded the dataset and contacting them.
You can also have a look at http://academictorrents.com to see if your dataset is present there.
