Traveling in Star Wars: The Old Republic is accomplished by using vehicles, taxis, shuttles, and starships. Also, at level 14, all classes are able to train an out of combat speed boost ability: Sprint.
Taxis[]
Taxis, or speeders, transport players between discovered locations on a planet for a low cost per trip.
Vehicles[]
Vehicles can be used to travel on a planet and can be summoned at will. They are available at level 25 and cost 
8,000 for the basic model. The training to use vehicles costs 40,000.
Shuttles[]
Shuttles give players the ability to travel between planets and fleets.
Starships[]
Starships allows players to travel between planets and complete space combat missions. Players can obtain their class-specific starship at the end of their class missions on Dromund Kaas (Empire) and Coruscant (Republic).