Depending on the type of site that you are running, it may or may not be advantageous to display search results instead of a 404 page, when someone visits a non-existent page on your site.

I believe that the site I've been maintaining recently would benefit from this as it is the site of a publication. With a publication the more people you can get to read your site the better.

But after reading up on how Google ranks the "quality" of your site, where you will appear in SERPs, based on how much the meta text of a page relates to the content of the page, I have to wonder if making a 404 page link to the search results would harm the "quality" of your site in Google eyes.