What your looking for is a media center, a little box, usually with a remote, you can stick a hard drive in and it'll play your videos for you.
The cheapest (and IMHO best) way to do this, if you have an old xbox lying around, is to softmod it. Then you can stick XBMC on (probably one of the most versatile media center applications ever) and use it to play all your DVDs etc. If you buy the right cable the Xbox can even output at HD resolutions via. Component Input (but if your source media is not HD, all it will do is upscale).
If you buy a commercial media center I would make sure it is Xvid/Divx compatible before committing to a purchase. Judging by your avatar, I'd assume you watch Anime, and seeing as most anime is encoded in Xvid ... you get the picture. This is partly the reason why the xbox is the best route, it can play almost every media, and any it dosent always have the potential to be added as its constantly updated. The only snag is it's a little tricky to setup.