Star Wars: The Old Republic is free to play this weekend. Starting on Thursday at 12:01am CT, you'll be able to create a new character and play up to level 15, and have access to Origin World, Capital World, the Fleet, all Warzones, and your character's first Flashpoint. No trading with other characters, though.
The free weekend comes to a close on Monday at 2am CT, at which point BioWare and EA will freeze your character in carbonite. If you decide you want to purchase the game, you may resume that character.