Short answer - it depends.
I've gone standby several times because I've changed my flight. Basically, they don't load your luggage until there is a space for you. Then, usually right before the flight takes off, they are certain that there will be room and they give you a boarding pass and load your luggage.
It seems (and makes sense) that the fewer number of people travelling together, the easier it is to get on the flight. Travelling alone, and being polite to the person at the computer, I always got on the plane. But, for the same flights I've seen couples have to wait for the next flight. So, if three people are going. I would group one parent with the child, and have the other parent on a different reservation.
I would also call the airline. They can look at their stats and tell you the odds of getting on via standby. Also, the flights that give you the best odds.