I don't mind compressed DVDs. There is absolutely no way I could keep much without compressing. Plus, I often stream them to a TV to watch with others, so with such a low res TV, they are fine. The MP3 compressed audio is probably worse than compressed video, but that depends what sound and what scenes it is.
1) I used to rip with DVD Decrypter and encode to Xvid with AutoGK. I knew it wasn't the best way to do it, but it was very simple to do. There are all these guides and software out there, but I didn't want to bother with it. So use this or read below if you want the quick and easy but effective way.
2) Now I use Fairuse Wizard. The free version limits you to 700MB file size and other things, but the full version is only $20, which is a kickass price. It is excellent. It will rip the DVD (to its own format) then encode, so you don't need other programs. I encode EVERYTHING to x264 now. IMO, and from screenshot comparisons, it is x264 > xvid > divx. I can't believe people still use divx. My x264 encodes look FAR better than the same thing in divx. I remember divx 3.11a encodes back with my Celeron 366@550, but that is just it: it is old as hell (though new versions must be better). Xvid became my new standard for the past few years until I started using FairUse and x264 for the past year or so.
I compress 2 hour or less videos to a 700MB x264 avi, 128kbps MP3 audio, with the slider all the way to Quality, using the highest resolution possible for that file size size and bit rate. I know a lot of people here wouldn't like that, but it saves a lot of space and looks awesome for the size. When the movie is much longer, I increase the file size so the resolution isn't so dang low (resolution limited by max possible compression ratio).
So, in conclusion, if you want to compress, I'd go with x264. Even my roommate's old G4 866mhz has no problem with x264 playback (though my encodes are no greater than 480p). I believe his Xbox with XBMC would struggle to playback x264, but I don't know for sure, but that thing is only a P3/Celeron 733mhz.
I guess I might not like compressed videos if I had a HDTV. But it will be years before I or roommates could afford one of those, so I'm sticking with x264. Even on my 1680x1050 monitor, they don't look much worse than a SD TV when you sit at least a few feet back like you would with a TV.
For pesky DVDs, use RipIt4Me with DVD Decrypter. If they won't rip to ISO in RipIt4Me (some won't, and FairUse can only use ISOs or it's own ripped format), rip to VOBs and use DVDShrink to create an ISO to load with FairUse. I don't use DVDFab Decrypter but it is mentioned a lot with these programs.