In the Datapoint 2200, each memory board had 32 shift registers, providing 2K of storage. The processor board used a counter to keep track of the shift register position, and would stop processing until the right bits were available. (Kind of like a cache miss in modern processors.)
I got a display board from a Datapoint 2200, which uses Intel 1405 shift registers for the display storage. This board uses 14 shift registers and holds 896 bytes. Shift-register memory was convenient for a video display board, since the circuitry needed to access each character in sequence to display it.
Details can be found on Ken Shirriff’s blog.