What movement abilities are there?
In addition to the below, all classes are able to vault, or pull themselves up, onto ledges and terrain, and of course can sprint and jump. There may be more movement abilities granted by exotic items and/or currently unseen subclass talents in the full game so this list may grow.
Titan has a jetpack as their jump ability across all subclasses. The jetpack provides an upward thrust when used and lasts a short time. Options to augment the jetpack include more height, more directional control or faster acceleration. The Striker subclass also has a shoulder charge which both deals damage and propels you a small distance forwards.
Warlock has a glide for their jump across as subclasses. The glide continues your momentum and lasts until you land on the ground or deactivate it. The glide differs from the Titan because if you are falling it will only slow your fall, not boost you upwards. Options to augment the glide include more height, more directional control or a burst of speed on use. In place of the more height augment, the Voidwalker subclass has the option to replace the glide with a blink, a short range teleport. The Dawnblade subclass has a perk in the top-most passive skill group that gives a mid-air dash.
Hunter has a double jump as well as a dodge roll across all subclasses. The double jump may be augmented with a triple jump, higher jump height or better directional control.