Formal:
* До свидания (Do svidaniya) - This is the most common and formal way to say goodbye. It literally means "until we meet again".
* Прощайте (Proshchay te) - This is a more formal and literary way to say goodbye. It means "farewell".
Informal:
* Пока (Poka) - This is the most common and informal way to say goodbye. It literally means "for now".
* До встречи (Do vstrechi) - This means "until we meet again" and is slightly more formal than "Пока".
* Всего хорошего (Vsego khoroshego) - This means "all the best" and is a good choice for a neutral farewell.
Other:
* Спокойной ночи (Spokoynoy nochy) - This means "good night" and is used for saying goodbye at the end of the day.
* Счастливо (Schastlivo) - This means "happily" and is a less common way to say goodbye.
The choice of which goodbye to use depends on the context. For example, you would use "До свидания" when speaking to a stranger or someone you are meeting for the first time. You would use "Пока" when speaking to a friend or family member.
Important Note: When saying goodbye in Russian, it is common to shake hands, hug, or kiss on the cheek, depending on the relationship between the people.