For CDs, I ripped them all onto my computer, as that's the only object I use for listening to music these days. Before that, I removed them from the jewel cases and kept them in binders, often with the liner notes in one pocket and the CD in another (essentially taking up two pockets per disc). I did generally keep the jewel cases, though, because the idea was that someday I would have more space and I would put the two back together. However, I could keep the jewel cases in inaccessible places.
For DVDs, I'm trying to do something similar, though I'm not technologically at the point where I can have all my movies be digital. So, I still have a lot of DVDs/Blu-Rays. I'm trying to put them into binders, and then I keep the cases in an inaccessible storage location, because someday I would still like to reunite them and display them on a shelf. I have one DVD tower where I still have DVDs in their cases, and unfortunately it's now become kind of a value judgment... Like, oh, this is one of my favorite movies, I'll keep it in the case on the shelf!
But I have so many favorite movies that this doesn't really work.
I have all the Sean Bean Sharpe movies on DVD, for example... That's 14 individual DVD cases, I think. I should just put them in a binder, get those cases off my shelf, and free up some space for the DVDs trickling onto my coffee table.