After doing a bit of research and working with other options, the best and easiest option I have found is a mix of SlySoft AnyDVD and SlySoft Clone DVD Mobile. I know there are a lot of other options out there, but I really find SlySoft to be the easiest to use for cloning movies. It's worth mentioning that there is ALWAYS a 20% off sale on the site, so don't feel pressured to buy it immediately.
Here's how it all works. SlySoft AnyDVD scans any disc you put in the computer, and removes and copy protection. It doesn't copy movies or anything, and it's clearly stated to use only for backups of movies. But all by itself AnyDVD isn't going to copy movies.
After you have AnyDVD running (it always runs in the background) you can use any program to back up your video. I prefer Clone DVD since it seems to be the easiest one, and the files that it makes are pretty small. I generally choose the iPod format, ten use the defaults for the rest of the options. It takes about a hour to coy each DVD, but then you can store it safely.