I have a 14 year old autistic son. He is non-verbal and somewhat higher on the spectrum than some of the persons described in earlier posts. He can ride a bicycle but only on our cul-de-sac as he can't quite get the concept of pedalling backward to stop.
I bought a tandem and at first he couldn't keep his feet on the pedals. I placed some toe straps and taught him to put his feet in them and now we can't be stopped. We have done some overnight tours and the tandem purchase has turned out to be a fantastic option. My son has no balance problems but for those that do check out the buddy bike
http://buddybike.com/.