Unless you live in a very, very small space, battery-powered lights will not cater to much of your lighting needs. But they can be useful sometimes. (The batteries I'm talking about in this post are made up of those small AAA, AA, C & D cells, the ones you use in flashlights and radios. 12 v batteries powered by wind/sun/hydro or gas is another story.)
These are my experiences:
Bulky camp light with fluorescent tube: These are retro for all the wrong reasons. They weigh a lot, use lots of batteries and supply astonishingly little light. Those key fobs with a single LED give out more light. There are some lights like this one out there with remote control, which is sort of nifty, but the D-sized cells and the fact that they don't really give off much light makes this a no-no, unless you happen to have one lying around anyway.
Traditional wardrobe light: These cost almost nothing, and are sold in just about every hardware store. In my experience, they are cheaply made and the incandescent bulb gives off very little light compared to the amount of batteries consumed.
New-fangled LED wardrobe light: These make quite a lot of sense. Even on the ones I use quite often, in dark corners of the kitchen, only need their batteries replaced every three or four months. They come with a lot of different fastening options, I usually choose velcro.
LED light w/ motion sensor: Motion sensors, it seems, have reached some threshold where they now cost almost nothing for those industrious Chinamen to make. I have several of these on the ceiling of my entrance/shop where they make themselves very useful. Though I say "shop" it's really just a glorified storage place for my tools, and I dip into often but very briefly to pick up some screwdriver or whatever. With these twinkling above, I don't have to don a headlight every time. It seems these lights do not react to Felis, the evil cat.
I have dreamt about hacking some of these to make "game cameras" (not that I'm going hunting anytime soon), but my imagination is better than my extracurricular (or "real", as I think of it) work ethic.
LED work light: These are sold in the kind of stores that sell equipment for cars, and are a real improvement over the traditional type with a fluorescent tube. They come with a 12 v charger, and have a quite good rechargeable battery inside. They give off a lot of light, but you need access to a car/an RE system or "normal" electricity. I have some of these in my doggy kitchen, makes more sense than routing cables all the way out there from the solar panels on the cabin.
I would write about batteries if I had anything to say that hadn't been said very well already.