So what ever happened to the holy kiss?
St. Paul commands the faithful to greet one another with a holy kiss (en philemati hagio) four different times in his writings. St. Peter uses similar language of a "kiss of love" (en philemati agapes; 1 Pet 5:14). This appears to be a non-liturgical practice, but something one would do when meeting another baptized Christian.
St. Ambrose Ambrose says that these "holy kisses" were exchanged publicly between members of the opposite sex. Tertullian recounts how a pagan husband was reluctant that his Christian wife should "meet one of the brethren with a kiss" (alicui fratrum ad osculum convenire, "Ad Uxor.", ii, 4).
This practice was formalized and included in the Holy Sacrifice of the Mass - perhaps the kiss of peace (not the handshake of peace) originates with the Apostles.
One of my favorite items from liturgical history are the various versions of the pax-brede. The pax-brede or pax-board was an instrument with a handle that had an image on it (often the Agnus Dei). First the celebrant kissed it and then the members of the parish would kiss it. It was a sort of "virtual" kiss of peace.
Today, the kiss of peace is exchanged formally between clerics by holding the elbows of one another and bowing forward twice - the first time to one side of the face, the second time to the other side of the face. When I was Anglican, I saw this occasionally. The picture above illustrates the practice.