Are 404 Pages Always Bad for SEO?

There are many different theories on 404 pages and whether or not they affect your websites SEO. Some people will recommend:

Do not allow them, 301 redirect any 404 error page back to the home page or category level page to protect link authority if an external site has linked to a non-existent URL.
Just do nothing and let incorrect URLs 404
Or do a bit of both, 301 redirect some 404 errors and leave others

Our opinion on this is the last of the above options. We believe that sometimes there are benefits in letting pages 404, for both users and search engines. It also does always make sense to just 301 redirect all 404 pages on your site, it does not seem natural to either your website’s users or search engines. But this does emphasise the importance of having a great, intuitive 404 page.

We believe that it is ok to let your website 404 unless the page receives:

Important external links to it (Google Webmaster Tools can be helpful for this)
A large quantity of traffic
Has an obvious URL that visitors/links intended to reach

So to summarise, 404 pages are not necessarily bad for SEO and there are cases where you should just let pages 404 as opposed to 301 redirecting them to other pages.