Our kids have a lot of toys. Good toys, but still-- a lot. Keeping them organized in our apartment is important for me so that I don't mind having so many.
Our solution, for now, is using storage bins and these modular white shelves that you can build to whatever shape you need. I am not in love with the unattractive gray bins, but since we've moved 8 times in 8 years, they are extremely functional, so for now- they will have to work. The one problem with the shelving is that it can come apart if you put too much pressure on it, and the bins are a little heavy.
An easy fix to that problem is using plastic cable ties (sold at Dollar Tree). I bought some at Wal Mart that are white and blend in to the shelving. I tied them tight and cut off the excess. In order to encourage the kids to keep the bins organized, I made labels for them by using my Cricut machine. I laminated the labels and taped them on using clear packaging tape. That way I can reuse them or rearrange them if necessary.
The labels made the kids excited all over again about each toy bin. My four year old is also excited because he is starting to read and the words, accompanying the pictures, on each label are making it easy for him recognize familiar words.