Disable back button in react navigation

1) To make the back button disappear in react-navigation

v5 or newer:

{     
    navigationOptions:  {
    title: 'MyScreen',
    headerLeft: ()=> null,
    // `headerLeft: undefined` should work too
    // `headerLeft: null` should work but could trigger a TS error
}

NOTE:
v6 has an extra option:
headerBackVisible: false​

Whether the back button is
visible in the header. You can use it to show a back button alongside
headerLeft if you have specified it.

https://reactnavigation.org/docs/native-stack-navigator/#headerbackvisible

v2-v4:

navigationOptions:  {
    title: 'MyScreen',
    headerLeft: null
}

2) If you want to clean navigation stack:

Assuming you are on the screen from which you want to navigate from:

If you are using react-navigation version v5 or newer you can use navigation.reset or CommonActions.reset:

 // Replace current navigation state with a new one,
 // index value will be the current active route:

navigation.reset({
  index: 0,
  routes: [{ name: 'Profile' }],
});

Source and more info here: https://reactnavigation.org/docs/navigation-prop/#reset

Or:

navigation.dispatch(
  CommonActions.reset({
    index: 1,
    routes: [
      { name: 'Home' },
      {
        name: 'Profile',
        params: { user: 'jane' },
      },
    ],
  })
);

Source and more info here: https://reactnavigation.org/docs/navigation-actions/#reset

For older versions of react-navigation:

v2-v4 use StackActions.reset(...)

import { StackActions, NavigationActions } from 'react-navigation';

const resetAction = StackActions.reset({
  index: 0, // <-- currect active route from actions array
  actions: [
    NavigationActions.navigate({ routeName: 'myRouteWithDisabledBackFunctionality' }),
  ],
});

this.props.navigation.dispatch(resetAction);

v1 use NavigationActions.reset

3) For android you will also have to disable the hardware back button using the BackHandler:

http://reactnative.dev/docs/backhandler.html

or if you want to use hooks:

https://github.com/react-native-community/hooks#usebackhandler

otherwise the app will close at android hardware back button press if navigation stack is empty.

Additional sources: thank you to the users that added comments below and helped keeping this answer updated for v5+.