I have recently released a new article on removing broken links focused on enterprise users, although for small scale SharePoint deployments this tool may be enough for anything larger than a few users I would suggest reading up on QIpoints excellent Broken Link Manager.
It’s a worthwhile investment to spend some time every once in a while making sure that within SharePoint, links that users may have added are not becoming broken as broken links can cause issues such as users no longer being able to find important information, navigation breaking down and images not appearing as they should. Not to mention the strong affect it has on user experience. In isolation these things may not cause too big of an issue but together they could spell doom for your SharePoint deployment.
The Search Engine Optimization Toolkit is a Microsoft product which can be downloaded here for free which allows you to check links for any website, but it also works very well within SharePoint.