One example would be the New World Jacamars and the Old World Bee-eaters both of whom look and act very alike through their adaptation to aerial hunting for insects.

Another example would be the Old and New World Vultures. Old World vultures are closely related to Hawks and Eagles while New World vultures are more closely related to Storks. Despite this, in looks and habits the two groups have developed remarkable similarities largely from the fact that they both depend on carrion for food.