I use it in everyday life occasionally (but I'm damned if I can think of an example).

Back when I was programming I used it when dump-reading. Say you have a printed stack of paper a foot and a half tall. You need to find a certain address in it, but you have no idea where it will be. So you split the stack roughly half way and examine the address - higher or lower? Then you split either the top half or the lower half (depending on which direction the address was), and repeat the process. It would only take 5-6 splits to find any address in the dump - very quick and efficient.