Whilst Google Webmaster tools can tell you whether a link is still working or not without you needing to visit every website you have ever linked to, a manual check every once in a while is strongly advisable.
Websites and domain names change hands all the time, and you may find yourself linking to inappropriate content. Unless a site visitor informs you of this, it can easily go unnoticed for months at a time, and may cause you damage to your credentials without you being aware of it.
You may also find that the link is no longer relevant to the information you are giving to your visitor, and it may be necessary to seek a better resource to link to.
Computers are all well and good for telling you simple things like “Linkrot has set in” but they can’t easily tell you if the content has changed from that which you and your site visitors were expecting to find. Better link housekeeping can improve your search engine rankings.
Find out more about link marketing in our SEO Book.