There are a few common misconceptions related to 404 pages and SEO that I'll attempt to clarify.
While it's common (and technically correct) to call 404 pages "errors," I am not a fan of that terminology. 404s are the expected result when a website is unable to return a given request, if there is no URL to deliver. If we wanted to be picky about it, we'd say 404 pages are not errors and can even be (blasphemy!) an acceptable user experience.
404s are fine. There's no need to panic. There's no need to "redirect every 404 to the home page" (eek!), the category parent, or your shopping cart.
All too often I hear SEOs recommending that every 404'd URL be redirected somewhere - anywhere - just so long as "the juice is captured." Nonsense.
I think people tend to freak out about 404s because they sense that Google will negatively score a site if they exist. Or, they worry that link equity is lost when quality links are pointing to a 404 page (a valid concern, which I'll elaborate on below).
Generally speaking (though there are exceptions), 404 pages are a very normal part of running a website. There's no reason to fret over them and there's certainly no proof (at least that we've seen) of Google or Bing penalizing a site for 404 pages.
When 404s Can Be "Bad"
There are cases, however, where a site could be scored negatively as a result of an abnormally high occurrence of 404 pages. Does your site have 10,000 unique pages but 45,000 404s this month? That could be an indicator of a bigger problem with crawling and technical SEO. That's also probably not a very good user experience, which could be reflected in poor user engagement and falling traffic, which could be reflected again by a search engine lowering visibility of your URLs in search results.
A high occurrence of 404s - when they are spiking and continuous - is not a good thing. But forget about SEO for a moment. Is that a good thing for users? Obviously not, and remember: search engines follow users.
Another potentially negative consequence of 404 pages is when a URL has valuable links. I'm not so rabid about "link equity" that I'm going to recommend every URL with links needs to be redirected. If there's not a good page match for a 404, don't redirect it. That said, if the links are precious and difficult to secure, think about contacting the site and having them update their link, or creating a new piece of content that's relevant for the existing link, or finding a relevant page that will still ensure a good user experience and 301 the page.
Last but not least, 404s can be bad news when they act like a 200. A soft 404 error page is not a good thing, because search engines will continue to index these.
Best Practices for Redirecting 404 Pages
Here is a quick list of best practices for redirecting 404 pages:
404s should not always be redirected.
404s should not be redirected globally to the home page.
404s should only be redirected to a category or parent page if that's the most relevant user experience available.
It's okay to serve a 404 when the page doesn't exist anymore (crazy, I know).
If you have valuable links pointing to 404 pages, do one of the tactics I outlined in the above section.
Don't panic. 404s are normal.
Bing's 404 page best practices: http://www.bing.com/webmaster/help/404-pages-best-practices-1c9f53b3
Google's 404 page best practices: http://support.google.com/webmasters/bin/answer.py?hl=en&answer=93641
Cool 404 examples: http://econsultancy.com/us/blog/9525-16-creative-404-pages-to-inspire-you-to-overhaul-yours
Another good resource on 404 pages and SEO: http://www.fallingupmedia.com/blog/404-page-examples-seo/