Fog machines also use glycerine and the instructions say "do not inhale fog". From Wikipedia:
Fog machines which generate their effects solely using water, such as ultrasonic or pressurized technology, pose no special health risks, however it should be noted that "water based" fog fluid does contain glycol. A number of studies have been published on the potential health effects presented by exposure to glycol based theatrical fogs and artificial mists. Two studies, a Health Hazard Evaluation completed in 1994 by the National Institute for Occupational Safety and Health, and another one in 2000 by the Department of Community and Preventative Medicine at the Mount Sinai School of Medicine and ENVIRON; both prepared for Actors Equity and the League of American Theaters and Producers, focused on the effects on actors and performers in Broadway musicals. The conclusion of both studies was that there was irritation of mucous membranes such as the eyes and the respiratory tract associated with extended peak exposure to theatrical fog.From the Actor's Equity study:
The report, jointly commissioned by Actors' Equity Association and the League of American Theatres and Producers, concluded that Actors are at risk when exposed to "elevated or peak levels of glycol smoke and mineral oil." However, it also noted that if exposure levels are kept below the limits established in the study, actors should "not suffer adverse impacts to their health or their vocal abilities."
At present it is not clear if e-cigs or glycol/glycerine pose a threat, and how much, but putting any foreign smoky substance into the lungs is, in general, a bad idea.
Actor's Equity study on fog machines and smoke.
Wikipedia glycerol (glycerine).
Wikipedia fog machine.
Zeecigs study on propylene glycol. PDF from 2009.
CDC: Toxic affects of glycol. PDF.