I have a lot-lot of outbound links on my webpage. A lot of them are broken, they point to 404 pages on external sites. I add to all links: nofollow.
Can it be possible that Google is penalizing me in search results? (I have a big result decreasing, I searching for reasons)
Google says 404 are not bad they don't hurt your site or someone elses
Do 404s hurt my site?
http://googlewebmastercentral.blogspot.com/2011/05/do-404s-hurt-my-site.html
If they are all outbound links external to other websites I would leave them it's not your site or for you to really worry about. At least the people are getting that much closer to the domain which once hosted the content they are looking for.
You should start logging these pages, and work on getting them cleaned up. If the pages were deleted, then 404 is ok. If they are moved, then you want to do the proper redirect to the new location (temporary or permanent).
I would block them in your robots.txt and also remove them from Google's index using the URL removal tool. I don't think they are bad, but they do make for a bad user experience. Another alternative is you could 301 redirect them to a new or similar page
If you are directing your users to 404 pages on other sites, your users are not going to be happy. For the sake of your users, you remove the broken links.
I was involved in the open directory project (dmoz.org) several years ago. One of the biggest problems that a directory site faces is broken links. The quality of the directory is based on how good its recommendations are. Broken links are the worst kind of recommendation.
I would recommend using link checking software to automatically scan all the links and find the ones that are broken.
From an SEO perspective, anything that is a usability problem is also an SEO problem these days. When users start preferring other sites over yours from search, your rankings fall.
