You need them whenever an address changes and something might still point at the old one. Changing a page name or the structure of your site. Moving from one domain to another. Consolidating two pages into one. Switching to secure addresses, or settling on one version of your domain rather than serving both with and without the leading letters. Each of those creates old addresses that exist in search results, in links on other sites, in emails, and in bookmarks.
The cost of skipping them is quiet and cumulative. Anybody following an old link reaches an error page and leaves, and the search visibility that address accumulated is lost rather than transferred. For a business that has been publishing for a year, that can be a meaningful share of everything earned so far, discarded during what looked like a routine site update.
Redirect to the closest equivalent page rather than to your home page. Somebody following a link to a specific service wants that service, and sending them to the home page to find it themselves is technically a redirect and practically a dead end. If genuinely nothing corresponds, a helpful error page offering the relevant alternatives beats a redirect that misleads.
Keep a list before you make changes rather than reconstructing afterward. Export your existing addresses, note the new one against each, and check them after the change by actually visiting a sample. Redirect chains, where one address points at another which points at a third, are a common outcome of doing this repeatedly without a record, and they dilute exactly what the redirect was meant to preserve.
Check for broken links periodically rather than only after a change, because links break for reasons that have nothing to do with you. A page you linked to elsewhere disappears, a partner restructures their site, or a resource you referenced moves. Free tools will crawl your site and list anything returning an error, and running that once a quarter takes minutes. Internal links pointing at your own missing pages are the ones worth fixing first, since those are entirely within your control and they signal neglect to both visitors and search engines.