I know that in the architectures I'm personally familiar with (x86, 6502, etc), the stack typically grows downwards (i.e. every item pushed onto the stack results in a decremented SP, not an incremented one).
I'm wondering about the historical rationale for this. I know that in a unified address space, it's convenient to start the stack on the opposite end of the data segment (say) so there's only a problem if the two sides collide in the middle. But why does the stack traditionally get the top part? Especially given how this is the opposite of the "conceptual" model?
(And note that in the 6502 architecture, the stack also grows downwards, even though it is bounded to a single 256-byte page, and this direction choice seems arbitrary.)
Stanley Mazor (4004 and 8080 architect) explains how stack growth direction was chosen for 8080 (and eventually for 8086) in "Intel Microprocessors: 8008 to 8086":
The stack pointer was chosen to run "downhill" (with the stack advancing toward lower memory) to simplify indexing into the stack from the user's program (positive indexing) and to simplify displaying the contents of the stack from a front panel.