Let's say you have a single web server you need to have up all of the time. You need high availability, but not necessarily instant fail-over, because you want to keep your costs low, and so you don't want two instances running all of the time. It may not serve much traffic at all, so there isn't much load to spread. What you can do is place an ELB in front of the web server, set a condition to start a new instance if the page becomes non-responsive (i.e., a failure), and set the auto-scaling to "min 1, max 1." This way, you'll always have a pool of one server, that will automatically rebuild if the instance fails.
I admit, it's not a common use case, but it's one of the more clever uses of the ELB I've heard. =)
