Here's a link to the Height Requirements Calculator we have on the DIS.
http://www.wdwinfo.com/wdwinfo/height.htm
I put in 38 inches and this is what it came up with.
Park Attraction Area Height
Typhoon Lagoon Bay Slide wave pool 52"
Magic Kingdom Big Thunder Mountain Railroad Frontierland 40"
Epcot Body Wars Wonders of Life 40"
DisneyQuest Buzz Lightyear's AstroBlaster 51"
DisneyQuest Cyberspace Mountain Create Zone 51"
Animal Kingdom Dinosaur DinoLand U.S.A. 40"
Blizzard Beach Downhill Double Dipper Left hand side of the wave pool 48"
Typhoon Lagoon Humunga Kowabunga Top of Mountain 48"
Animal Kingdom Kali River Rapids Asia 38"
DisneyQuest Mighty Ducks Pinball Slam Score Zone 48"
Animal Kingdom Primeval Whirl DinoLand U.S.A. 48"
MGM Studios Rock' n'oller Coaster Starring Aerosmith Sunset Boulevard 48"
Magic Kingdom Space Mountain Tomorrowland 44"
Magic Kingdom Splash Mountain Frontierland 40"
MGM Studios Star Tours 40"
Blizzard Beach Summit Plummet Top of Mountain 48"
Epcot Test Track Future World 40"
MGM Studios The Twilight Zone Tower of Terror Sunset Blvd. 40"
Magic Kingdom Tomorrowland Indy Speedway Tomorrowland 52"