Speed-wise in order, the common gaits are: walk, trot (this is the bouncy one), canter, and gallop. Here's what the link has about the TW gaits:
The Tennessee Walking Horse performs the flat foot walk, running walk, and canter. These three are the gaits for which the Tennessee Walking Horse is famous, with the running walk being an inherited natural gait unique to this breed. Many Tennessee Walking Horses are able to perform the rack, stepping pace, fox-trot, single-foot and other variations of the famous running walk, while this is not desirable in the show ring the above mentioned gaits are smooth easy trail riding gaits.
The flat foot walk is a brisk, long-reaching walk that can cover from 4 to 8 miles an hour. This is a four cornered gait with each of the horse's feet hitting the ground separately at regular intervals. The horse will glide over the track left by the front foot with his hind foot (right rear over right front, left rear over left front). The action of the back foot slipping over the front track is known as overstride. Overstride is unique to the walking horse breed. The hock should show only forward motion, with vertical hock action being highly undesirable. A Tennessee Walking Horse will nod its head in rhythm with the cadence of its feet. This nodding head motion, with the overstride, are two features that are unique to the Tennessee Walking Horse.
