arigatou / arigatou gozaimasu (polite)
ありがとう ･ ありがとうございます
You can also say domo/Thanks when talking to friends
And domo Arigato gozaimasu for extra politeness and emphasis.
If you're watching shows / reading manga / etc, you'll also see things like 「すみません」 (sumimasen) and 「たすかった」 (tasukatta) translated as "thank you," though the literal meanings are more along the lines of "sorry for the trouble" and "you helped me," respectively. I'm sure there's others.
Unfortunately, I'm not yet pro enough to really understand when each of those forms would be considered more appropriate. Probably won't go wrong sticking with a basic "arigatou gozaimasu" while you're just learning.. mostly just keep in mind that there are other forms that mean effectively the same thing when you hear them, even if the literal translations sound a bit strange.