Rulers start at zero:
At zero centimetres, you have nothing, whereas at one centimetres, you have one unit of length. Memory is similar: You start filling at the beginning (zero), hence, the first x-memory units contain x units of data, the next unit contains unit x+1.
Distances in boardgames with discrete spaces. For example: Chess, wargames, Dungeons & Dragons played on a battlemap, etc. Counting movement, the space you start in counts as space zero (or more accurately: if a piece stays in the same space, then it has moved zero distance).
There are a number of situations in wargames and RPGs where two pieces might ...
The ground floor is the de facto 0th floor.
Humans are born at age 0.
Military time starts at 0:00. Despite the day having 24 hours, it is not correct to write 24:00.
As a side-note, Japanese TV uses 0-indexed 12-hour notation. That means 11 AM is followed by 0 PM, not 12 PM.