Formal:
* Muito obrigado (male)
* Muito obrigada (female)
Informal:
* Muito obrigado (male, used for both genders in informal situations)
* Valeu! (informal, more common in Brazil)
* Obrigado(a)! (less formal than "muito obrigado(a)")
More expressive:
* Obrigado(a) de coração! (Thank you from the heart!)
* Agradeço muito! (I appreciate it very much!)
You can also add "por tudo" (for everything) after any of these phrases for a more comprehensive thank you.
Example:
* "Muito obrigado por tudo!" (Thank you very much for everything!)
Remember that Portuguese has two major dialects: European Portuguese and Brazilian Portuguese. While the phrases listed above are generally understood in both, some regional variations exist.