It appears to me to be a "throw away" preposition in most cases. There is no loss of meaning without it.
You may want to pay attention to cases where the preposition is really attached to the verb. Take, for ex., the case of someone talking about when they will be broadcasting a show. "To be on the air" means to be broadcasting:
We'll be on the air June 29 at 6 p.m.
We'll be on the air on June 29 at 6 p.m.
We'll be on on June 29 at 6 p.m.
We'll be on June 29 at 6 p.m.
We might hear any of the four. In the last one, because the utterance is so abbreviated, the speaker will make sure there's no pause between "be" and "on," (be'on), to signal their connectedness.