Most wireless routers can act either in access mode or as a bridge. Some can act as both at the same time.
I would seriously question "most"!!
Perhaps that is true of currently available products, but unlikely to be true of stuff more than a couple of years old - and stuff lying around in cupboards is unlikely to be new.
For example, the ubiquitous Netgear WGR614 is now at v9, and it is ONLY v9 and above that supports WDS (Wireless Distributed System), Netgear's implementation of built-in wifi repeater funtionality. v9 was released in 2008, I believe.
Only 3 Netgear wifi routers (as opposed to access points only) supported WDS 2 years ago, and six by mid-2008.
To add to the problem, many ISPs implemented bespoke firmware on the routers provided to end users, and removed or crippled some functionality. I am aware of one major UK ISP that removed the WDS functionality from the WGR614 v9.
Finally, the WDS feature is not completely specified in IEEE or Wi-Fi standards, therefore interoperability between 802.11 products of different vendors is not guaranteed. The same is probably true of other vendors' offerings.
So in summary, the chances of being able to delve into a cupboard of cast-off ISP-specific wifi routers and make up a working extended wifi-repeated network are very low indeed.
However, simply cascading one device from another via a physical ethernet connection - as per GG's original suggestion - is almost guaranteed to work, irrespective of the make, model and firmware of the devices.
I've not tried those mains-borne devices but I've heard good reports about those, too. I don't know if you can hook a wireless access point onto one, though.
Keef - of course you can, no problem. It's just another ethernet node.
SD