I use old 2 litre ice-cream containers for my scrap storage, one for a colour or group of colours, as well as one for novelty/multi-coloured scraps and one for felt scraps.
I also use a bigger container for white scraps (which I use a lot of), and an even larger container for batting scraps. The long strips from trimming a quilt before binding end up in here, anything larger than about the size of my laptop is folded and stored with my batting yardage. I also have a WIP scraps bin, which sits on my worktable - I throw bits in there as I'm working on something and then sort them into colour in a batch.
The advantages of using ice-cream containers are that they are stackable, they have lids, they're free and it's easy to change the number of containers you're using. You could start with, for example, four containers but as your scrap stash grew you could extend it to eight (for example), and it wouldn't cost you anything other than maybe a few inches around the waist and half an hour to re-sort your scraps. The downside is they're not pretty.
Some tips I have for scrap storage would be to trim off loose thread and odd pieces that aren't of a usable size, and press them so they're (hopefully) usable straight out of your scrap bin.
So that's mine - it's not pretty, but it works really well, and so long as you've got someone in your house who eats an awful lot of ice-cream then in no time at all you'll have enough containers for your scrap storage. I totally agree with Sarah when she says it's worth keeping your stash beautifully organised, it really does help you actually use it.
I'm very excited that I'll be linking up, for the first time, to Sunday Stash at Molli Sparkles - hello Glitterati!! If you're new here, why not take a look around my Scraps 101 series to see what I've been up to lately.