In Orthodox Christianity, the customary funeral has an open casket and a point where people can come up and venerate (kiss) the deceased. From what I understand this is a very old practice. There's not much emphasis on making them look asleep though, often foregoing embalming and just getting them in the ground pretty quick.
You just reminded me of a funeral for a high school friend who was killed in the 9/11 attack on the WTC. The coffin was closed the whole time until at the grave, the Greek Orthodox priest opened it a little for some anointing ritual. There was an audible gasp among those present (most of us present weren't Orthodox), and I remember his mother trying to get a peek inside. Someone who had a better angle said that inside the coffin was another coffin since presumably his remains were in no shape to be seen.
