They release vapors that contain nicotine into the atmosphere. There has been comparatively little study on the dangers of second hand nicotine vapor vs. secondhand smoke, but I would be hesitant to assume that there is no danger.
I could also imagine that they could reduce the social pressure against smoking, as people would be seen happily puffing away on e-cigs which, from a distance, look an awful lot like regular cigarettes. Impressionable kids, people who have quit smoking but may be tempted to go back, etc. will now see smoking suddenly becoming socially acceptable again. Some people may see it and think that smoking is allowed wherever this is, and then light up a real cigarette.
There's a further sort of puritanical attitude that many people have towards smoking, I think due to the fact that it was so prevalent and so obnoxious for much of the 20th century. Much as some people have a puritanical attitude about drinking (and we still have ridiculous laws stemming from that), that attitude may persist about smoking even if e-cigs turn out to be much less obnoxious than cigarettes.
You have to remember, there are plenty of people who were non-smokers during the middle of the 20th century, when you couldn't go to a bar that wasn't saturated in smoke, where you had to breathe in secondhand smoke almost everywhere (even in the non-smoking section of restaurants, it would still waft over from the smoking section), where if you lent something to a smoker it would come back reeking of smoke. The idea of losing ground on the fight that was just recently won, of not allowing it in most indoor public places, makes non-smokers fairly anxious.
Now, if it can be demonstrated that secondhand vapor from e-cigs is perfectly safe, and that it doesn't permeate the air with the same foul smell, then maybe their introduction would be welcomed.
After all of the damage we've done over the years by rapidly accepting new technologies that wind up poisoning the air (see, for example, secondhand smoke, leaded gasoline, diacetyl, asbestos, the Great Smog of '52 and the continuing smog problems in Beijing today), we need to be less willing to simply assume that releasing something into the air we all breathe is perfectly safe, and instead only allow it once it has been demonstrated to be safe.
As far as I can tell, e-cigs only started becoming popular in the last few years. While I'm fine with people using them in their own homes or outdoors (since there's a certain level of concentration below which it's not worth worrying about anything), I'd be very skeptical of accepting them in establishments in which smoking is not allowed without further study.