It depends on the circumstances and the publisher. In many cases publishers permit authors to host the accepted version of the paper (but not the final version that includes revisions based on reviewer feedback) on their personal/institutional website and to email copies of the paper on an individual basis to people who request them.

For example, see https://www.elsevier.com/about/policies/copyright (under "Author Rights") for what Elsevier permits you to do with your own work.

On the other hand, publishers have sometimes filed lawsuits against sites where authors share their papers, e.g. ResearchGate: https://www.nature.com/articles/d41586-018-06945-6

Elsevier have also sent takedown notices to universities where academics have made the final version available on their institutional websites:

https://www.washingtonpost.com/news/the-switch/wp/2013/12/19...

https://osc.universityofcalifornia.edu/2013/12/elsevier-take...

https://news.harvard.edu/gazette/story/newsplus/elsevier-tak...

https://blogs.library.duke.edu/scholcomm/2014/01/28/setting-...