That depends on where the 404 errors are? Are you linking to pages that don't exist? If so, make sure you fix the links.
a) It sure won't help your rankings
b) Visitors might get frustrated following links to pages that don't exist.
If the 404 errors are for resources being called. (i.e. a image, js library, etc) then it is less likely to effect your SEO directly, but it will slow down your page loading a bit. The browser will try to download the file, get the error response, then move on to the next file.
404 status code errors are soft errors and you can easily check them in "Google Webmaster tools". Large count of 404 error pages sometimes cause problem. For better, you can get a "custom 404 page" for great user experience.
It depends on the page on which 404 error occur. You need to remove all the links from your website which generate 404 error pages. If those links are from third party websites like social bookmarking, directory, articles, blogs etc. you should create a 404 page and redirect users to that page whenever any 404 error occur. It there are lots of 404 errors then they can be harmful to your website ranking.
As per Google, 404 errors doesn't effect you ranking much but it will give you a sad user experience when the site has bunch of 404 errors and ultimately you will suffer with these errors because Google mainly focus to give the users best search results and they wont allow rank pages, which provides poor user experience. But it is very easy to remove 404 errors by connecting your site to webmaster tools.