We use this as an early warning of an attack as it is the electronic equivalent of the door being rattled or the lock being tested.
When 404 errors breach our thresh-hold we block the originating IP address. We subscribe to the Blacklist Repeat Offenders list and HackRepair.com, a known list of hackers. The list is permanently banned, and updated as new offenders are identified.
Of course 404 errors can also indicate broken page links or missing images and so this also provides a useful tool to make sure your website is kept up to scratch.