I've seen this expression probably a dozen times in anime and manga. There are many variants, but they all have the character's tongue sticking up out of the side of their mouth. Their eyes are also typically big and sometimes in the shape of a backwards の character, or sometimes winking. Here are a few examples, though there are many more:
Bakemonogatari:
Clannad:
Tonari no Kashiwagi-san:
What is the origin of these expressions? Are they referring to a particular art style or character?
All of these faces are direct parodies of Fujiya's forever 6 year old mascot, Peko-chan:
Peko-chan was created in the 1950s is probably the most recognized character in the Japanese confectionery world.
In Japan, showing one's tongue can be used to express one's feeling embarrassed at making a mistake. It's often times meant to be childish and regarded as cute. There are no solid references connecting the behavior to Fujiya's mascot, but some believe the behavior is popularized by children imitating Peko-chan.
For me, the Clannad and the Tonari no Kashiwagi-san pictures at least shows more an attitude of "tasty!" / "it's good!" expression: the tongue sticking out is just one licking its lips to get all the remaining gravy / taste, and this is enhanced by the hand gesture showing appreciation.
These are quite universal body expressions.
