No it doesn't, just as long as it's not a 404 HTTP btw. If you're not sure whether it's a "404 Not Found" or a "404 HTTP" code then you can simply use the Fetch as Googlebot feature in Webmaster Tools to double-check.
If you have some links on your site that no longer exist, don't stress too much, that won't affect how your webpages perform in search results.
However, it will not be good for the user though. So the best thing to do with 404's is to create a 301 redirect for the old URL to a new URL.