My older son first rode Splash Mtn, Big Thunder Mtn, and Goofy's Barnstormer when he had just turned 3. He loved them, and I didn't feel that he was too young to handle them. I'm not quite as sure about Space Mtn (he's now 4 and meets the height requirement), since he can't sit next to me or my husband, and it's completely dark. We may wait until he's 5 or 6 for that one, and we're definitely waiting until he's older for Mission Space.
My younger son was 36" when we went to WDW last time (he was about 22 months), but I didn't want him to ride Goofy's Barnstormer. I think that it is a bit too jarring for such a young child. We're going again next month (he'll be 2 1/2), and he's probably about 38" or 39", and I'm undecided about letting him ride it. The seats are hard, and my older son still bumps the back of his head on it.
That being said, if you need a fix, your son can ride most of the other rides. We needed a fix after our first child and we went when he was 18 months. He certainly doesn't remember it, but he did enjoy it at the time.