Google Webmaster Tools reports "not found" URLs. These are links on other websites with spelling mistakes. Often the site owner does not react to my suggestion for correction. What to do in these situations? Is it a good practice to redirect (301) non-existing.html to existing.html?
Forgive me, I don't quite understand the question, and may be misinterpreting.
"Links on other websites,..." - These are links on other websites to specific pages on your site?
IF site owners do not make the correction needed, THEN you definitely need to take action, IF you are relying on the link for your users.
It reads as though they are linking to a page on your website, but a typ0 is causing a '404 - Not Found'. In this case, the simplest solution, IMO, is to '301 - Moved Permanently' - even if the referenced page never existed. The typ0 URL on the website can be allowed to stand and the user will be sent directly to the correct page.
This bypasses the site owner, and you still get the full benefit of the link.