Software blog MakeUseOf actually shares two different methods within the GIMP to "cartoonify" your portraits—one involves a built-in cartoonifying tool, and the other involves manually tweaking other settings like Threshold and Value. They also share a method using the Edge Detect feature to create a similar effect on non-portraits (that is, photos of objects and not people). It's a pretty neat tutorial, and if you play around with it enough, you can actually get some pretty cool-looking shots. Hit the link for the detailed instructions.
How to Cartoonify Your Photos With GIMP [MakeUseOf]