For trout fishing, I am forever changing how I store my too many flies. I switched from boxing flies by type to boxing flies by fishing location (I don't get out much) a few years ago, but it never seems to be what I want.
For steelhead fishing, I've used the same 3 boxes for years, and it's worked out great.
1. Regular wets go in a standard Wheatley clip box. The sides of the box have large clips and both sides of the leaf has smaller clips. (I generally don't buy nice things like a Wheatley, but this one was a gift for my fly club service.)
2. Muddlers go in a fleece fly wallet.
3. Steelhead dries go in a cheap Plano box with 7 compartments (3 long compartments and 4 half-size). I had them in an inexpensive waterproof (gasketed) box, but I'm having my kids use that box now, since they are much shorter than I and hence more prone to getting fly boxes wet.
One could certainly get by with fewer boxes, but I like to tie flies, and this is certainly sufficient and organized for my purposes. Since the 3 boxes are so different, I am never confused and never pull out the wrong box.
--Bill