The villager disappearing bug is well known, but it is frequently attributed to the unloading/loading of the chunk that the villager is in. I want to show that the villagers can disappear even when the chunk is constantly loaded and a player is standing nearby. Attached is a clip where you can see a villager disappear while I was standing right in front of it. I've also made the clip into a gif and linked it here: http://gfycat.com/CornyComposedArmyworm

This clip is unedited, no cuts were made. The villager literally disappeared while I was looking at it. Afterwards I attempted to place a pressure plate on the block where it was standing to see if it was a visual glitch. The pressure plate did not activate, indicating that there was no entity in that block. I also restarted my client to confirm that this wasn't a visual glitch. The villager still wasn't there upon re-log.