I strive to design my caricatures with a foundation in reality. That means I like the faces to look correct anatomically, with a painterly sort of realism, even though they are pulled and stretched beyond realistic proportions.
The most important element to a caricature is the likeness. With humor being a close second. It needs to look like subject or else it is not a caricature. If done really well, a caricature will look more like the person than they look like themselves while making you laugh, or at least chuckle a little.
Here is a gallery of caricature illustrations and portraits. They are all painted either digitally or with oils on canvas.