Call them "steppers" or "spinners" or "spin boxes," but we've all seen and used these things:
Now, in a touchscreen environment this type of control might be useful, if the touch targets are large enough. Also in situations where the range of possible numbers is very small and benefits from more description and specificity, I can see them being useful. Hotel guests, quantity of items in a cart, number of airline passengers, etc:
(we won't get into the proximity issues with the above implementation)
BUT: Numeric stepper controls are often attached to text fields for numeric input, particularly in desktop use. There seem to be a number of problems with them, such as the Fitt's-Law-challenged tiny click targets and already noted issues of affordance and limited standardization of their secondary input methods, such as typing, using the mouse, keyboard up/down arrows, etc.
But if these are in place of or augmenting a numeric input field, and the user can simply type the exact value they want into the field... what's the point of having the stepper at all? Is this just a useless input control for this situation? (Ok, look, I know it's not completely useless, just for this situation). Can someone give me good reasons to use these things as part of a text field? Are there any good studies on actual use and engagement with these things?