Kitchen (and bathroom) cabinets usually have what is called a "toe-kick" - the area between the floor and the bottom of the cabinet. The toe-kick is most often recessed - and guess what? There's nothing there but space waiting to be used.
You can do this in a rented apartment as long as you are careful - take your time, and you'll end up with an awesome stash spot.
Best of all, this doesn't cost more than a buck!
Here's what you need to get started:
Putty knife with a thin blade
Some sort of pry tool, putty knife with thicker blade or flat piece of metal
A trim tool - used to pry molding from base boards
Diagonal cutters or tin snips
Hammer or mallet
File and sandpaper
Block of wood to protect the surface you're going to hammer
Vacuum cleaner or broom (optional)
4 rare earth magnets
Four screws or nails with heads - make sure they're attracted to magnets
Small piece of thin plywood (optional)
Box or other container to fit the spot (optional)
Step 1: Identify the Spot
The baseboard needs to be a separate piece of wood, i.e., not attached to the cabinet itself. Most floor cabinets are set up this way.
Step 2: Carefully, Carefully Pry Off the Board
Begin by scoring between the adjoining boards to separate the paint (if it's painted), so that nothing peels or chips. Then take the putty knife, and gently work it between the boards from top to bottom. Try not to pry, but to loosen. Keep working your way from top to bottom, wiggling the tool as you go. As soon as you've got a clean line, pry gently until you can fit in the thicker tool. Do this on both sides if you have access - mine was next to the stove, so I had to work from one side. I strongly advise against using a screwdriver, as they are prone to putting big dents in the wood.
Once you get the board moved about 1/4", you can put one end of the tool against the inside of the board and give it a couple of taps with your hammer. Keep working like this until you can fit your fingers in the space.
Then start pushing the board back and forth with your hand, being careful not to break or crack it. This can take awhile if the space is tight, so be patient. It's okay to bend the nails, and once you get it far enough out, you can bang on it with the hammer.
Eventually you'll be able to pull the board completely off. Yay! Look at all that room!
Step 3: Clean and Inspect the Space
I also like to put something on the floor - usually cardboard or a scrap of carpet. Underneath my cabinet, the vinyl flooring had been cut and tucked in, so I tacked that down just to make everything smooth.
If your cabinet is one with a drawer on the bottom, chances are it will have a dust barrier, which is a piece of wood underneath the drawer. If it doesn't, the space is still secure - but you can add a piece of wood if you want.
Step 4: Prepare the Board
Take your diagonal cutters, rotary tool or hacksaw and cut the nails close to the board, and file them so they don't bite you later.
Now, poke starter holes below or above the nail stubs, and slowly drill a little recess to insert the magnets. Be extremely careful not to drill through the board.
A neat little woodworkers trick is to wrap a small piece of tape around the bit at the right depth. That way all of the holes will be the same depth.
Test fit the magnets until they are perfectly flush with the board. If you drill too deep, just put a piece of cardboard or scrap of something in the hole to shore it up. When they are flush, glue them in with epoxy, and double check that they're still flush.
Now you're ready to work on the cabinet itself.
That's it, the board is ready!
Step 5: Put the Screws In
To mark the spot, I put the screws on the magnet and pressed it against the cabinet frame.
Drill pilot holes - slightly smaller than the diameter of the screws, then put those puppies in. You want them as flush as possible and still able to grab the magnets. As you're driving them, watch weather or not the wood is starting to split. If it is, back out the screws and drill a larger hole. If the hole is too big, just glue the screws in.Keep checking your work until you get it right and everything from the outside looks nice and tight.
Step 6: Stash Your Stuff!
Step 7: Final Notes
Finally, the toe-kick board may be pretty darn tight. Mine was way too tight, so I filed and sanded the top of it off until it fit just right.