Is there a plugin, similar to https://wordpress.org/plugins/broken-link-checker/ or other Wordpress plugins, that can test links in the database and report which ones are broken? It doesn't have to be pretty or fancy.
nystudio107 has a great plugin that takes care of this and lets you implement redirects when broken links are found.
(I don't think retour actually looks for broken links actively - it does log 404s coming in to your site though and make it easy to set up re-directs).
There are a number of online services that will spider your site and report on broken internal or external links - e.g. https://www.semrush.com
I am not aware of a plugin for Craft that does this directly by looking in the db as such.
Can't seem to find a plugin that does this. I may build a link into the CP dashboard for a third party link-checking service like https://validator.w3.org/checklink, http://www.deadlinkchecker.com/website-dead-link-checker.asp, or http://www.brokenlinkcheck.com/. Or just recommend a browser extension that will do it on a page-by-page basis, like Check My Links for Chrome.
Maybe once I get into plugin development, I'll make one myself. :)