Are there any good alternatives to the Wayback Machine that also archive a large part of the web?
Coming from academia, I myself primarily use The Wayback Machine. In research literature I also encounter some use of WebCite (http://www.webcitation.org) in references.
Anyone interested in web archiving, might have a look at introduction to web archiving at wikipedia, including an overview of web archiving services: http://en.wikipedia.org/wiki/Web_archiving
If the past version of the page you are looking for is <3 months old, you could also try cache:URL in google search (or equivalent function in other search engine).
For sufficiently recent dates, web caches can serve a similar purpose. Some of those can be accessed conveniently using the Firefox plugin "Resurrect Pages" (https://addons.mozilla.org/en-us/firefox/addon/resurrect-pag...).
You can preserve the present version of a site for yourself. No tool will work for all sites, but some tools will work well for many sites. WebHTTrack is good. It will record the address and date of each capture.