Formal:
* Obrigado (male)
* Obrigada (female)
Informal:
* Obrigado (male)
* Obrigada (female)
* Valeu (informal, more like "thanks")
* Obrigado, obrigado (male, very informal)
* Obrigada, obrigada (female, very informal)
You can also use "muito obrigado" (male) or "muito obrigada" (female) for "thank you very much".
For a specific thing, you can add a preposition:
* Obrigado por... (Thank you for...)
* Obrigada por... (Thank you for...)
For example:
* Obrigado por sua ajuda. (Thank you for your help.)
* Obrigada por me ajudar. (Thank you for helping me.)
Remember to use the correct gender (male or female) depending on the person you are talking to.