Formal:
* Нет, спасибо. (Net, spasibo.) This is the most common and polite way to say "no thank you."
* Нет, благодарю. (Net, blagodaryu.) This is also polite and can be used in more formal settings.
Informal:
* Нет, спасибо. (Net, spasibo.) This is also used in informal settings.
* Не надо. (Ne nado.) This means "no need" and is a more informal way to decline something.
* Спасибо, но нет. (Spasibo, no net.) This means "thank you, but no" and is a good way to politely decline an offer.
To emphasize your refusal:
* Нет, спасибо, не хочу. (Net, spasibo, ne khochu.) This means "no thank you, I don't want to."
* Нет, спасибо, мне не нужно. (Net, spasibo, mne ne nuzhno.) This means "no thank you, I don't need it."
Remember that the most appropriate phrase to use will depend on the situation and the person you are speaking to.