It is different case by case and it depands on the location and the importance of the avatar in the specific situation.
The highest importance is probably in the user profile screens. In this detail screens, users expect larger and more detailed picture. Can be higher than 120-180px.
Another good place to use big avatar is list app (contacts or messaging apps) because the avatar is used as Guidance element. For example skype is about 80px, Facebook messenger about 120px.
Third option is the place where the avatar is actualy not very important. It can be inside the conversation thread or in the social app feed. In these cases the most important thing is the content so that the avatar is quite small (about 60px for FB, Skype and Instagram).
// The px sizes are from iOS apps and only tentative!