I know I've seen that age restriction listed for the Barnstormer, too. But I also know that my dd was tall enough before she was 3yo and rode on it.
As Gail mentioned, the Speedway has an age restriction....from what I can remember from last week, its 1 year. I think its very important on that ride that the child be able to sit independently....with the risk of being bumped from behind. To drive alone, kids must be 52"....and as with all rides they must be 7yo to go alone (ie. without a parent or other adult) and I have seen CM's ask children how old they are before allowing them to ride alone on anything.
They also will not allow younger siblings to ride with an older child on any ride....I saw parents being called up to Dumbo because they had sent their 3yo to ride with their 7yo. The 7yo was allowed to ride alone, but the 3yo needed an adult. I think that may be related to an incident on another ride where a small child fell out because there was no adult riding along to assure that the usual safety precautions were met (ie. all body parts kept in the vehicle and remain seated....)
Otherwise, I'm not aware of anything else that has an age restriction. My dd has always been allowed on everything she was tall enough for...and she's a tall child. We also rode Kali River Rapids before she was 3yo...they just have a special seat for smaller kids.