The Eggbutt Snaffle is probably the most widely used snaffle bit. The name comes from the somewhat egg-shaped connection between the mouthpiece and the bit rings.
The main benefit of the eggbutt shape is that the chance of the lip being pinched between the mouthpiece and bit ring is lessened. As you can see, the mouthpiece itself widens out at the sides, and the join between the mouthpiece and the ring is distanced from the horse's lips.
This shape makes the bit less mobile than the loose-ring snaffle -- the mouthpiece doesn't move quite so much in the horse's mouth.