You probably haven't been losing any sleep wondering about this, but in the digital age, a snooze alarm could be any length of time. It's nine minutes because of the limitations of tehcnology when the alarm was invented:
Alarm clocks in 1956 had standardized gears. The snooze gear needed to mesh with the teeth of the other gears. Due to the configuration of the gears, a 10-minute snooze cycle was out of the question, so the engineers had to choose between nine minutes or 10-plus minutes.
And we live in America, chock-full of that whole Protestant work ethic, so the engineers went with nine minutes. Don't dare be late for work or you'll end up a miserable failure.
The nine-minute interval carried into the digital age. Some early digital clock designer probably took a look at an old mechanical clock and decided nine minutes was the standard.
Love my snooze alarm. On work days, I set the alarm for just over an hour before I have to get up -- that's seven snooze alarms. But that means you have to wake up eight times in one morning, say the morning-loving ntwits who like to bound out of bend and tackle the day with zest. But I get to go to sleep seven times in the same morning -- that's the point.