Inverting colors in Paint is not something I do frequently. But when you do need this feature occasionally, I have the point of view that Paint is the best tool for such basic image editing. Few days ago, I needed to create a header image for my Youtube channel with a line of inverted colors. I am a Windows power user, yet I was really confused by the user interface of the modern version of MS Paint (I use Windows 8.1).
Starting with Windows 7, the Paint application ships with the Ribbon UI. It looks fancy, but when you need to invert colors of your image, you will not find the appropriate command on any tab of the Ribbon nor in the File menu.
The required command is hidden inside the context menu of the drawing area. Moreover, the context menu containing the "Invert color" command is only available when you have the "Select" tool chosen. Click on the "Select" tool and then right click on the image you are editing and you will find it:
Bonus tip: You can also invert colors only for a selected area. You can select a portion of your image, right click on the selection and use the context menu command, 'Invert color'.