Woven Open Top Storage Bins
While there's a seemingly infinite number of ways you can choose to try to store your child's toys–which unfortunately seem to pile up and multiply on their own when you're not looking–we've been most happy with these simple woven bins that don't scream "toys" and could actually be used for anything from blankets to magazines to hats and mittens (which we also use them for).
We originally got our black ones here, but they don't consistently carry them, so this is a link to similar ones in a similar size.
The open tops make it easy for your child (and you) to remember what's in each bin... Magna-tiles? Duplo? Matchbox cars? Stuffies? And the softness and handles make it easy for your child to drag it around wherever they need it :)