The problem wasn't with OSPF (Open Shortest Path First) [1]—it was with the port settings [2].
Sigh.
I keep forgetting that on Cisco routers, interfaces named “Ethernet” are only 10Mbps (Megabits per second), while “FastEthernet” are 100Mbps. Also, 10Mbps interfaces are not full duplex, but half duplex.
Now that I've made those changes, the problem seems to have gone away.
I have to remember: Ethernet are 10Mbps, FastEthernet are 100Mbps.