Okay, I remembered to snap a few pics.
I am the opposite of RCC1 above (his is what my shop aspires to some day) and this thread will no doubt become a testament to my extreme disorganizedness (if that ain't a word, it is now).
Since you asked about drawers specifically, the only drawers I have with AR parts are some of the filing cabinet drawers out in my shop which have furniture pieces in them (mags in others, etc.)...
And lest you think my disorganizedness (there's that word again!) is limited to the AR platform...
Most of the parts and pieces out in my shop are in old baby diaper boxes (older stuff) and Rubbermaid bins of assorted sizes (newer/more important stuff)...
Some of them are labeled, but most are haphazzard an unorganized...
Uppers waiting to be used are in padded boxes, usually the ones they were shipped in...
FTR, most of my ammo that isn't in the house or in the garage is also scattered about in that same shop...
Since the "shop" is just being used for storage at the moment and is no condition for me to work on guns there (yet!), I do keep some parts in the house. Some of it is in smaller bins...
But the essential small parts are kept in tackleboxes, and can go to the range or a class with me if need be...
FWIW, fixing up the shop and building more shelves and a nice work bench is a project I hope to complete before the end of the year... I had really hoped to do it this past summer, but higher priority stuff kept getting in the way.
Some day...