Really? Any one I have seen have been an adsl modem and a switch joined together. The switch ports don't care whether they are connected to a computer or another switch. The ports or all bi-directional or you couldn't build a network.
Logically a typical UK home router can be thought of as a combination of FIVE different network devices.
1: an ADSL modem
2: a router with NAT capabilities
3: a DHCP server
4: an ethernet switch
5: a wireless access point.
You also get home routers that omit the ADSL modem and have an ethernet port on the WAN side. These are often known as "cable routers" as they were typically used in conjunction with cable modems (in the days before virgin media supplied combined modem-router units)
There are actually at least ways you can have a setup with two home routers.
One option is to disable the DHCP server in one of them, set them to different lan-side IPs from the same subnet and connect their lan sides together. By doing this you make the second router act as a mere switch and wireless access point, the modem and router functionality in it are not used (they are still there but no traffic will ever reach them because no computer will have it's default gateway pointing at them).
The second option is to put a NAT router behind a NAT router, to do this you need a router whose WAN-side port is ethernet. You also have to configure the routers so their LAN-side networks use different IP ranges as most routers don't like having the LAN-side, an advantage of this approach is it provides some (though not total) isolation between the networks. The downside is that the traffic is NATed twice which can cause problems with some applications.
The third option is to put a router behind a router but without using NAT on the "inner" router. Again you will need a router where the WAN-side port is ethernet. You will also need to add a routing table entry on the "outer" router so it knows about the inner router.
It was a common problem on office networks that people would plug the lan-side of a home router into the office network without disabling the dhcp server and it would cause chaos as it handed out bogus IP and gateway information. So-much so that many managed switches have explicit functionality for blocking unwanted dhcp servers.