In the Eastern Orthodox Church, <snip> it is appropriate and common for laity to greet clergy, whether priests or bishops, by making a profound bow and saying, "Father, bless" (to a priest) or "Master, bless" (to a bishop) 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."
I've tried kissing Anglican bishops hands, mostly they seem surprised. My very good friend the late Bishop (Thomas) Richard Hare (1922-2010), had enormous fun with it. I would kiss his hand, and he would say "but I haven't got my ring on", then I'd explain again that it was his hand I was kissing. He was noted for his phenomenal memory, so I know he didn't need reminding. One day he quickly reached into a drawer beside his chair and put his bishop's ring on just as I rose to leave - I deliberately missed the proffered ring, to kiss his hand. We laughed. My old profile photo is one that he took of me on the couch at his cottage. Memory Eternal, Richard, and do pray for us.