IOS routers can act as DHCP clients and DHCP servers. They can also function as Network Address Translation (NAT) devices. In this video we show a demonstration using a 2621 as a DHCP client, server, and NAT translation device for my home network.
It's important to understand that most IOS routers have relatively slow CPU's. An IOS router is fine as a DHCP server for a few dozen clients. But if you try to serve thousands of DHCP clients you are likely to fail and suffer an outage.
IOS routers can also work as a network address translation devices. IOS NAT is "ok" but for real high capacity NAT (thousands of users) you want to use a device designed to handle high capacity NAT. PIXes, FWSMs, and ASA's are excellent NAT devices.