In the Roman Catholic Church, a Catholic meeting the Pope or less often a Cardinal, or even a lower-ranking prelate, will kiss the ring on his hand. Again this has become uncommon in circles not used to formal protocol, even often dispensed with amongst clergy. However it is still more common in the more demonstrative Mediterranean cultures, especially the Italian baciamano. Sometimes, the devout kisser combines the hand kissing with a genuflection as an even stronger expression of filial respect for the clerically high-ranking father. The cleric may then in a fatherly way lay his other hand on the kisser's head or even bless him/her by a manual cross sign. In the Catholic Church, it is also traditional for the laity to kiss the hands of a newly-ordained priest after his inaugural mass, in veneration of the Body of Christ, which is held in the priest's hands during the Holy Eucharist.
In the Eastern Orthodox Church, throughout the world and even in America, it is appropriate and common for laity to greet clergy, whether priests or bishops, by making a profound bow and saying, "Father Bless" while placing their right hand, palm up, in front of their bodies. The priest then blesses them with the sign of the cross and then places his hand in theirs, offering the opportunity to kiss his hand. Orthodox Christians kiss their priest's hands not only to honor their spiritual father confessor, but in veneration of the Body of Christ which the priest handles during the Divine Liturgy as he prepares Holy Communion. The profound bow is frequently omitted. A similar ritual occurs when an Orthodox Christian approaches an icon he wishes to venerate. First the Christian makes a profound bow and makes the sign of the cross twice. Then he approaches the icon more closely, kissing the icon, usually on the representation of Christ's, or the saint's, hand or feet. Lastly, he will make a final profound bow and make the sign of the cross. Orthodox theology teaches that, honor given to the Virgin Mary, ascends to him who was enfleshed by her. This applies to saint's relics or icons and in this case, to the priest's hand. Lastly, it is a common practice when writing a letter to a priest to begin with the words "Father Bless" rather than "Dear Father" and end the letter with the words "Kissing your right hand" rather than "Sincerely."
The hand kissing is used quite prominently in The Godfather series, as a way to indicate the person who is the Don.
At times, a hand kiss is also used to parody the things it traditionally stands for. In this case the kisser would likely initiate it, as a mockery of the situation or the other person.