Comment by HeyLaughingBoy

It's been long enough ago that I don't use it as an interview answer anymore, but one of the most interesting things I built (technique-wise) was a Z-80 based serial multiplexer with no RAM. The only volatile memory it used was the device registers. The fun part was handling subroutine calls without a stack. The Z-80 has an indexed jump mode, so before calling a subroutine, I'd fill the jump register with the statement after the subroutine call, and when the subroutine was done, execute the jump with the (return) address prefilled.

Anything to save a few bucks on a 6264 SRAM component :-)