On the Output tile of CloneDVD, instead of sending the data to the DVD writer, click on ISO/UDF Image. It'll then copy all of the files off the disc, package it all up nice into one .iso file. The .iso file will be a copy of your disc, and will be ~4.35GBs if you chose the DVD-5 option, or ~9GBs for the DVD-9 option. Then all you'll have to do is mount the iso file (using Virtual CloneDrive or PowerISO or any other similar program) and it'll work as if you just put the disc into your computer. Some programs, like VLC Player, will let you open the iso & play its contents without mounting. You should be able to use your prefered DVD burning software to then burn the iso (possibly called image) later if you prefer to have a physical backup as well.
Depending on the program you chose to play the discs back, you may want to chose DVD Files instead of ISO Image on Clone DVD's output tile. Rather than collecting everything into one nice .iso file, you'll get a VIDEO_TS folder & all the various .vob, .ts, etc files you'd find if you opened the disc through My Computer... I'm pretty sure Windows Media Center likes it this way. Just make a C:/My Movies folder, tell CloneDVD to copy to that folder.. Go into WMC's settings & tell it your video library is there. Then when you click "Play DVDs" you should get a listing of all the titles you've got in there & clicking on one will start it up just like if the disc was inserted.
Another method that may work for you, again, depending on how you plan to use your library, would be to use Clone DVD Mobile. You can use it to rip the movie (&/or additional features) to your computer in various formats. These files will generally be smaller in size than the entire DVD image from above, so you'll be able to store more movies in the same space. You can also opt to select a format that'll work with various game consoles (XBox, PS3), smartphone, etc so you could watch your library on the go as well.