Our method of simplifying our CD collection involved getting an iPod. We were getting aggrivated with 1) the sheer amount of CDs (I was scared to count, but we combined our collections when we moved in together, and had to purchase a huge unit just to house them); and 2) the kids getting into them and using them as projectiles, which not only unorganizes them, but destroyed a few of them, too.
So I spent a weekend putting all of the CDs onto the iPod. We have since boxed up the CDs and put them into storage. The only reason I haven't sold them yet, is that I'm nervous about the mp3 player screwing up. But so far, so good. They're backed up on the computer, as well. And I've been meaning to look into it to see if they can be burned onto DVDs as another backup method (it should only take a few DVDs)
The iPod is great, because it eliminates so much clutter, and it saves time. Instead of tracking down the CD, keeping my fingers crossed that the right CD is in the case, loading the CD into the player, then trying to remember to put it back afterwards...I simply plug the iPod into the stereo. As a bonus, I can drag my entire CD collection down to the laundry room and plug it into the old stereo I have in there. Or I can drag the entire music collection into the car. Or take it to work. Or on the bus. You just can't do that with CDs!
I really do love this system.
But if you want to hang onto the CD's, I'd recommend a binder with removable sleeves. And I'd sort them alphabetically, because I know I'd be more inclined to flip through it that way, rather than trying to figure out what genre an obscure artist is.