Load balancers are shipping
Example #1: Server down
The first example of when someone needs a load balancer is when a server crashes. For some websites, this means they're gone. For a load balanced website, this means that the traffic starts hitting the other server(s) and the users have no idea that something happened.
Example #2: Server slow
Sometimes, a processes goes in an unplanned direction and uses a ton of resources. This presents a more difficult problem - the server responds as if it is up, but it just doesn't perform well. That means that the load balancer needs to watch what's going on (response times) and not just who's next in line that I can still ping.
Example #3: Heavy usage
When your website starts to get too many users at once (as ours does at times), no single server is going to really be able to handle it. By load balancing, multiple servers can be used to spread the load across multiple machines and make sure that as needs grow the site can scale. This, combined with the zero downtime, is our primary reason for going to load balancers. Instead of needing HUGE servers, we can get by with multiple smaller (and much less expensive) machines to create higher availability and faster response times.
Example #4: Excess money
This hasn't been the case for us lately (moving is expensive), but I think some places just like using load balancers because they sound cool and they've got extra money to throw around. We tend to only buy what we need right now instead of wasting money, so we can keep more of the money in our customer's pockets and not have to raise prices too much. I'm sure many of our customers appreciate that. :-)