There are commercially available (here in Oz, they are all over the place! - including 'cheapariums') 'CD/DVD storage boxes' (you can get 3 types - one specifically for each, and one that will 'serve for both types') around - they tend to have a slight gap between each storage slot. These are intended for 'normal commercial CD/DVDs - some of those special cases including the wider ones that hold sets won't fit.

I have some as wall mounted open things - and some as drawers. They mostly seem to be made of mdf board, but I have seen 'plastic ones' - these days 'everything comes from China' here...

If you are talking about 'naked CDs' there are many vinyl 'carriers' around that have lots of little sleeves.