I've gone through a number of different storage solutions for our diapers in the last few years. With infant twins, you go through A LOT of diapers, and you have to have them within reach at all times. No time to go to another room to grab a diaper when one baby is screaming about a dirty diaper and the other because she is tired! Although my girls are now fully potty-trained for daytime, they still use diapers for naps and at night, and I have stuck with this system because it keeps everything together, and the girls can help get things and put them back themselves.
My diaper storage solution: a bathroom caddy.
I keep the diapers and a changing mat in the two bigger compartments, and wipes and diaper cream/lotion in the other two smaller compartments. Now that the girls are older and less than thrilled about putting on a diaper, it helps them feel like "less of a baby" to be able to choose their diaper (sidenote: I always get the cheapest brand now because they aren't wearing them except to sleep. They still like picking them out even when they don't have different characters or designs to choose from!). Having the diapers stored this way allows them to do that more easily. Having the other necessities easily accessible has also been really helpful. And especially when they were younger, it was awesome to have it in a caddy like this. Instead of having to open a drawer or closet, I could just take the caddy to whatever room we were primarily using at the time. SO much easier!
How do you keep track of your diaper supplies? Do you have a system you like to use?