Java %= and general feedback
I have no problem with +=, -= and even *=. But for /= and %=... perhaps I am just not used to them enough to like seeing them. I would recommend not using %=, but that is mostly my personal preference.

Other comments:


Instead of using the heightInInches as a field of the class, I would recommend passing it as a parameter to the method. Your method is only dependent of this single variable so I don't really see a reason to having it dependent on your class, especially since your method actually modifies this variable. You'd be much safer in having your method as

public String getHeightInFeetAndInches(int heightInInches) {


You could even make your method static if you would like (which I personally would recommend)
Your VALUE_OF_ONE_FOOT should be static as it is a constant value.
It is totally impossible for your leftOver value to be less than zero unless your heightInInches is also less than zero. And so far I haven't seen a single person with a negative height. Did you mean if (leftOver &lt;= 0)?
I would have the last space as a part of the includeInches variable, as if it would be empty right now your return would end with a trailing space.
Please use more spaces and make this line }else if(leftOver &lt;= 1) { into } else if (leftOver &lt;= 1) {
As @palacsint has pointed out, your code has a serious bug. I believe you should use the following:

int leftOver = heightInInches % VALUE_OF_ONE_FOOT;
int newHeight = heightInInches / VALUE_OF_ONE_FOOT;


This would also have the benefit of not modifying your heightInInches variable (although I still think you should pass it as a parameter to the method instead of using it as a field).
As pointed out by P. Lalonde in the comments below, your VALUE_OF_ONE_FOOT should be renamed to something like INCHES_PER_FOOT. All constants are values of something.
Feature Request: Add support for the metric system ;)