Love Alpine. The biggest use case I've found for small images so far is for testing a microservices system on Travis or a similar CI. You package each of your services in a container, then use docker-compose1[1] to start everything up. The faster it can pull down the images, the faster your CI build runs, so size can be important here.
One interesting thing about Alpine is that it uses MUSL[2] for its libc. If you want the bare minimum image size, you can use a scratch or busybox image and statically compile your binaries[3].
[1] https://docs.docker.com/compose/
[3] http://blog.xebia.com/create-the-smallest-possible-docker-co...