A recent post on the subject of cordless lights generated this great suggestion from a reader named tr: Sylvania's LED Dot-it Lights.These puck-like 3-LED lights are battery-powered (each ones takes 3 AAA batteries) and the flat side is finished with a 3M adhesive, so you can stick them on the inside of a closet (or any awkward space where you need light) without worrying about cords. You push an on/off button to operate them and they give off a white light that's "brighter and longer lasting than standard incandescent tap lights. " The batteries need to be replaced after about 100 hours of use.
A caveat: we've been warned that the adhesive does not part ways with your wall easily when it's time to change those batteries, so you may want to just find a more temporary way to install them in your closet, like slipping them into the clear pockets of an inside-door organizer.
Now let's see some bedroom closets!