I thought you could call field.getValues() to get all the field's values as an array. Then, you'll be able to count the number of values inside the array
so you would need to do something like
var values = MV_field.getValues();
var nrOfValues = values.length;
getValues() is indeed not the right way to get the items, although the naming does look confusing.
The solution proposed in the accepted answer does return the number of items fields, but might be risky
If i have a multi-value field with two items, and click the plus icon, but don't fill in any value, then the statement
var count = fieldObj.getElement().parentElement.children.length - 1;
returns 3, although, the actual number of values is two (as i didn't fill in a third value yet.
I did some quick testing and debugging with the gui extensions, and found out you can also get the values like this
var fieldBuilder = $display.getView().properties.controls.fieldBuilder;
var count = fieldBuilder.properties.dataRoot.getElementsByTagName("MultiValueField_Name").length;
That gives you the exact number of values entered, and also gives you direct access to the items (as an xml object).