Planetary travel: You can use shuttleports and starports to travel from city to city on a planet's surface.
You can also use your own ship (a fighter, freighter, luxury yacht, etc) to travel between starports on a planet.
A special type of transport vehicle is available to anyone who purchases the SWG Starter Kit - the Instant Travel vehicle. You can use this without a shuttleport or starport. You use it to pick you up in remote areas and transport you to any shuttleport or starport on that planet's surface.
Interplanetary travel: You can use a starport to travel to other planets. You can also simply use your own ship to travel to other planets. That's a cheaper (costs you nothing) and quicker way to travel around the galaxy.
Launching into Space: With Jump to Lightspeed added to SWG, an entirely new sphere of play opened up. You can launch into space from a planet and monkey around that planetary system in your ship. Depending on your faction, you can select different missions to do in space. Every player, regardless of profession, can be equally effective in space combat. Many people play the game just for this alone: I myself am addicted to cruising around in my X-Wing and dogfighting in space.
Another cool element: space combat is most definitely multiplayer. If you have the certification to fly the Millenium Falcon class of freighter, you and your group can man the ship in space. Your buds can man the turrets while you fly, for example.
You gain certifications to fly various starships by doing space quests and working your way through the Pilot profession. Pilot is a secondary profession at this time, meaning it is available to all characters regardless of primary profession. My goal is to gain the certification to fly the Jedi Starfighter, a sleek, and very cool, starship.
(the X-Wing is clunky and slow compared to this one)
Starships have oodles of components and systems, so it's possible to improve your ships (you can have more than one) as you complete quests, salvage the wreckage of your foes in space, or make purchases from vendors on planets. Player Shipwrights can create hulls and all kinds of components. You can dock at space stations and repair your ships when needed. It's all quite nice and engaging, and perhaps the best part of SWG to date.