Is there a 'standard' on how to number components?

I'm referring to the way reference designators for components are placed.
If people (engineer, designer, assembler, technician) want to see a Right,
Down method, would that apply to the schematic or the board?  If there is
no stanrdard, I'm sure it all boils down to whatever the people involved
agree upon.

I was wondering what the popular concensus is...anyone?