What are some examples of devices that would use the Z80's bus request input?
From the technical manual re. BUSRQ:
Input, active low. The bus request signal is used to request the CPU address bus, data bus and tri-state output control signals to go to a high impedance state so that other devices can control these buses. When BUSRQ is activated, the CPU will set these buses to a high impedance state as soon as the current CPU machine cycle is terminated.
I'm assuming this rules out memory as whatever address is present on the address bus would disappear when the CPU enters high impedance (w/ regards to the bus).