I use static IPs for network devices which are "lower level" than the DHCP server. Specifically, my router has a static IP, my switches both have static IPs, and my Hyper-V box uses a static IP (although all of the VMs use DHCP).
This way, basic network functionality can exist if devices get rebooted and a DHCP server isn't available. For example, after a loss of power everything comes back online and the network is properly functioning after a very short time. The box that does DHCP takes longer to boot than the switches do, so I've found that it's best that they don't use DHCP.
So, if you're average-joe-user, DHCP is for you. But there are certainly still places where static IPs make sense. It's just that you don't get there until your network gets a little bit complicated.