In the Event Log, you will see event IS 1020 from source DhcpServer. An example is below.
Event Type: Warning
Event Source: DhcpServer
Event Category: None
Event ID: 1020
Description: Scope, 192.168.16.0, is 100 percent full with only 0 IP addresses remaining.
The DHCP server also has a log file located at %systemroot%\DHCP. The problem is that this event will not be listed there. For a complete listing of all events for the DHCP Log, browse to: http://support.microsoft.com/kb/298367
Class: 6421A Configuring and Troubleshooting a Windows Server 2008 Network Infrastructure