I know you have seen those kits without a bottom box, they only have the sides open, and you slide the sprues out, and if you do it more then once or twice, you have busted off a piece or two.
Now me I take the real small pieces and put them in the small medicine vials, and I put a strip of tape around it marking the number of the kit to keep track of what is in there.
Now the bigger pieces I put in the bigger vials and keep them separate so they won't break the small pieces, cause you know how fragile them small pieces can be.
Of coarse I take off the old prescription message that was on there, and with the bottle almost transparent you can just about see what your looking at, I don't know if somebody else already suggested this, but this is what I've been doing for a long time, and it works good for me, I've lost a lot fewer pieces after I started to do this.
Especially on the kits that open from the side with no bottom.

I use 35mm film canisters and medicine bottles for the small parts and tupperware containers for the sprues.

i have a little storage unit with clear pull out trays in it for small things and larger tubs/containers for bigger bits. those takeaway plastic microwave trays with the lids are pretty handy too.

kitbasher :-)

My favorite storage container is yogurt cups. They have clear tops to see right inside, so the need to label them is nonexistant. And they are of a descent size for bigger pieces.

I use a number of things ranging from medicine containers (which in my place are very abundant) to tupperware containers ( "borrowed" from the kitchen, and yes dear, I promise to return them) to small clear plastic jars with snap lids that I've been able to smuggle out of work (but saying they are not being used for anything, what's the big secret????????)

i went to lowes and went to the tool box isle and they have a wide variety of storage options in a wide range of prices. I have one standup 'screw/connector' holder chest and three flip top divider boxes for various 'things'.

I used to use the meds bottles but when I downed three German Cantenes for a head ache I decided to stop.

#:-)

I use Zip-lock bags with a white rectangular panel that I can write on. If I have smaller parts, I can put them in smaller bags inside the larger bags.

Sealhead

I only got 2 tupperware and I use them for paint booths to dry in on the primer, see I got 7 models on hold now waiting an airbrush when I get enough money, I'll get an airbrush, but in the mean time even though I can see thru the bottles I got to mark them which kit is which, now some parts will tell you right off, but some of them real tiny parts, and you got 3 wheeled vehicles, I don't know about you, but I haft to keep track of them.
After the primer drys I put the bodys back in their boxes cause I can't afford new paint dryers, cause I'm starting another 2 hummers, and things keep adding up.
Now sense it was working so good for me I just thought some others that wanted a good place to store tiny parts, these are ideal, and don't take up much space.
But you can do what ever you feel like.

i use almost every thing i could find usefull
from shoebox, empty paint jar, chocolate box/can, pencil box

my fav is tamiya paint bottle .. good to store 1/35 gun/riffle/helmet/head..etc..etc

Film cans and yogurt cups???? Give me a break.

Go down to Walmart, Lowes or any hardware store and get some "parts bins" -- basically a rack with little plastic drawers in it. I have three of them and need more. I use paper labels on the drawers to tell me what's inside.

For models I am actively working on, I like to use those little foam meat trays -- they are usually white or black, so you can see the parts that are ready, but not attached to a subassembly yet.

If I'm building one of those kits with the end-opening box thein it's simple - tape the end shut and cut round three sides of the lid. For storing 'spare parts' I have four old model boxes - figures, accessories, aircraft and vehicle parts. Left overs from new models go in these and reclaimed parts from old busted kits. I know roughly what's in each box, just annoys the rest of the family when I rattle around in the boxes during TV soaps!

I use a variety of things. But for keeping small sub-assemblies safe, I've taken to using empty Altoids (or similar) tins. I have a co-worker who sits next to me, goes through Altoids like, err, candy (ahem). So I started grabbing the empties (though at 6 or 7, I felt I had enough for a while). Wash them out, line the insides with masking tape or Parafilm-M to avoid things getting scuffed against the metal. Convenient and durable!

Randy

My two boys build Warhammer models and figures. The container that the parts for the figures come in is a 3 sections styrofoam box (2 small sections and 1 large section0. The containers are approx 4" x 6". Just the right size for the smaller subassemblies. The larger pieces I keep on my modeling desk. To keep my cats off of the workdesk, I keep a jar of Testors liquid cement slightly open. The smell keeps them away.
If anyone lives near a "salvage" store. Sometimes you can find those small plastic cups they use in hospitals to give you asprin.
For keeping parts together in those pesky Testors and others "slide" boxes. Check your local craft store for small opaque plastic parts boxes with the snap lid. Also there are fishing lure boxes with many small compartments.
Whenever I go out shoping with my wife I look at everything with an eye towards its usefulness in modeling. I have been wanting to try eyeshadow as a drybushing experiment.
Lots of colors and shades plus metallic colors.