This is an easy activity for babies who can reach out and grasp things:
Get the baby’s attention by wiggling your finger, and when he reaches out to grab it, do some slow evasive maneuvers. Let him catch your finger from time to time also, to avoid frustration.
This is a great activity to promote hand-eye coordination, and it also stimulates the connection between the two lobes of the brain if you cross from one side of the body to the other.
[...] Finger chase. If your baby is a little older you can use a toy, but make sure she gets a few chances to nom on it, too. [...]