OpenStreetMap is a large dataset that is and always has been open. Also, Project Gutenberg and archive.org.
The initiatives that stay open tend to be the ones that were specifically set up with the intent of being open, and organize themselves accordingly (as not-for-profits with the "open" part written into their charter, for example). Anything set up by a for-profit corporation will eventually either die or be turned into an income source. A single person collecting data that's of interest to them is a crapshoot influenced by their individual ideals and how much money they get offered. The problem, as usual, is people, not technology.
There are a few types of data that absolutely should not be open, however. Most health data falls into that category.