One important use is as a source of reliably-dated prior art. The authors discuss admissibility and authentication issues. Two additional points not made in the article:

• Technical experts may reasonably rely on dated web pages from archive.org.
• In addition to web pages, the Wayback Machine also contains a substantial amount of software with datestamps — a potentially good source of software prior art.

[Way]Back to the Future: Using the Wayback Machine in Patent Litigation
By James L. Quarles III, Richard A. Crudo

http://www.americanbar.org/publications/landslide/2013-14/january-february/wayback_the_future.html