With the Joomla! component Dynamic404 you can redirect 404-pages to other URLs easily by using a 30x-redirect. This way, visitors will never get an annoying 404 Not Found page anymore, but they will be redirected to the right page. Alternatively you can setup a solid 404-page which actually helps your visitors find the right page.

Getting started
Purchase a Dynamic404 Support Subscription
Download and install the Dynamic404 component in Joomla!
Download and install the Dynamic404 System Plugin in Joomla!
Optionally install extra Dynamic404 plugins
Enable the Dynamic404 System Plugin
Setup Dynamic404 to your needs
Optionally configure statis redirect-rules
Screenshots
Want to see Dynamic404 in action?

Benefits
Never loose visitors due to unusable error pages
Migrate from older Joomla versions while maintaining SEO
Short URL marketing as a bonus
User Reviews

Dynamic404 is definitely not only useful but is in my arsenal of plugins I won't build a site without. Actually, it's the only one that is consistently needed for any site, regardless of what the site is for. I do recall I was a bit confused at first on how to get it to redirect the way I wanted it to, but I'm not sure there is any room for improvement on that. Maybe re-wording or displaying the instructions a bit it differently? It didn't take me long to get it though! If there were any more or any less features it just would not be perfect but it indeed is. I even downloaded a very expensive app that claimed to take care of all of the 404 issues I may have; but I discovered after fumbling with it for 2 hours and contacting their support, it would not do the two basic functions I downloaded it for, despite being bulked up with a bunch of useless features. I got my money and shortly found Dynamic 404 and haven't need anything else since!
Erica Burrell
Note on third party SEF solutions
Please note that third party SEF solutions like sh404SEF or Artio JoomSEF are not supported, because they ship with their own 404 mechanism.

What Dynamic can do for you?
Dynamic404 makes Joomla! error-handling smarter. It tries to redirect your visitors to the right page instead of showing the normal error-page. When determining which page is the closest match, it uses some fuzzy logic when searching for Menu-Item aliases, article aliases and other useful data contained in your Joomla! database.

If no redirect-match is found, the normal error-page is shown. Alternatively, you can configure redirects yourself from within the Joomla! Administrator. This way you can even fix URL-typos made by your visitors.