Router configured (intentionally) with no default routes? Would one ever find a router that had been intentionally configured to not have any default routes? No default gateway, no `0.0.0.0/0`... Sort of an academic question, someone at work mentioned it, and it seems a bit crazy to me. Even large backbone routers would need to have a default route if they had an address they didn't recognize... I don't know much about BGP, so I may be shooting myself in the foot here.

As Ron Maupin pointed out, this is not uncommon. It's especially used between autonomous systems speaking BGP, and there actually is a thing called the "Default Free Zone", the core of the internet in which no default gateways are configured: all routes are exchanged via BGP.

Not having default routes there actually serves a purpose: it prevents traffic to unallocated destinations to be discarded at the first possible hop, so it will not bounce between networks.