I feel like something needs to be explained, as some people might not realize that there are multiple aspects to archive.org, and that various posters may not all be referring to the same things.
The Internet Archive - The Archive itself, founded in 1996 with the purpose of archiving the web. In 1999, it branched out beyond this when it became the online home of the
Prelinger Archives. Since then, it has grown to host many (in my opinion) interesting and culturally valuable collections, including images from NASA, propaganda materials from all sides, rare books previously only available for viewing in the research libraries that housed them, and much more.
Wayback Machine - Digital archive of the WWW. The Archive began archiving web pages in 1996, and the Wayback Machine became available in 2001.
Open Library - a digital lending library with the additional ambitious goal of building a web page for every book ever published.
Additional projects can be viewed here.
Now, to examine things a bit further: The main Archive's collections include public collections, to which anyone can contribute. These are the collections which are troublesome in terms of potential copyright violations.
Problematic items do sometimes end up in the tightly curated collections, but that is generally the result of incomplete records and limited access to original source material. Several foreign films, for example, have been in and out a few times due to lack of clarity on whether or not they were "GATTed". As I mentioned in a previous post, there are many mid-century American films that, despite having registrations and renewals on file, fell into public domain immediately due to being released without the appropriate copyright notice required at that time.
There is also a lot of original content on the Archive, released into PD or with a CC license by the creators. Some items are there by express permission. This is more common in the audio collections.
It's almost as though the Archive exists as two realms - one in which users / contributors have an "anything goes" attitude, and the other where they spend days trying to ascertain the status of a single item. Many collection forums have endless listings of users attempting to research copyright status. The collections I spend most of my time in are unlikely to end up with problematic material unless it's placed there by accident. If I was actually seeking popular, recent items, there are much easier ways than trolling the Archive.