The main advantage of using DHCP reservations is that the assignment of a "static" IP address is managed centrally. This can be helpful for example if you are often rebuilding a particular computer or constantly changing the OS or if setting a "static" IP address is cumbersome (DirectTV DVR for example).
Using DHCP reservations is also handy if you ever need to migrate to a new subnet. In most cases then you just need to change the subnet on the router\DHCP server and all the clients will automatically be updated to the new subnet.
Lastly, using DHCP reservations is nice because you have a central place that you can go and lookup the IP address of a machine, provided the router\DHCP server allows you to note a name in addition to the IP address and MAC Address.
The down side to DHCP Reservations is that you have to know the MAC address, not a huge deal, but depending on the Router\DHCP Server and the computers OS it may be more time consuming that just setting a static address on the machine.