Thanks for writing us, Elaine,
You may be surprised to find that many attractions at WDW don't have height restrictions, but for safety reasons some certainly do.
For great info on traveling with little ones, including a list of attractions with height restrictions, please click
HERE and download the pdf file "Attraction Height Requirements" on the top right of the page. It includes attraction height requirements for all four theme parks, the water parks, and DisneyQuest.
If an attraction isn't listed on this document it means that there is no height requirement and any age/size child can enjoy the ride. One exception (perhaps because it is so new): the "Sum of All Fears" attractions at Epcot's Innoventions East isn't listed, but has a 48 inch requirement for all, and 54 inch requirement if you select to do any inversions.
The height requirements are also listed on all the maps at the parks and on signage in front of most attractions.
Hope that helps!