Question

Assuming, that a user has written some text into an EditText and thereafter touched somewhere else on the screen, which caused the cursor position to change: How can one determine the new cursor position?

Answer 1

The simple version:

myEditText.getSelectionStart();

If you want to react on an event you may try

myEditText.setOnTouchListener(new View.OnTouchListener() {
    @Override
    public boolean onTouch(View view, MotionEvent event) {
        // view is myEditText here
    }
});

event allows to distinguish between presses and releases.

EditText also has a setOnClickListener() that might be worth to look at.

EDIT:
I forgot to mention onSelectionChanged(int selStart, int selEnd) where selEnd equals selStart if the position changed.