It's not about the load balancing software itself, say HAProxy or Nginx, but with ELB AWS autoscales and handles failover between availability zones. You could certainly handle spinning up your own LB instances, managing DNS/Elastic IPs to handle failovers, etc. It would be far more expensive in setup time, management time and EC2 bill, than ELB which is practically free, starting at less than $20/month.

Among different datacenters this is done most often in DNS in order to avoid the increased latency and singe-point-of-failure.