Basing this answer on piano - clue in question!
Playing a scale one octave only means most of the time, you'll play the highest note (r.h.) with pinky, wheras playing two, or three or more octaves necessitates 'starting again', where your thumb, usually, goes onto the tonic for the next octave each time.
So with that in mind, two octaves seem like the minimum. But why not carry on to three, or maybe four? In more advanced playing, your hands will become farther apart, so you're setting yourself up for when this happens. The arms' angles change, which means even simple scales will be played subtly differently.
From memory, I think scales on piano for exams go to three octaves in the higher grades, so that seems a reasonable target.
If, by any chance, you're considering the question relates to other instruments, there are many good reasons to play as many octaves as the instrument (and player!) are capable of.