In the past, it seemed generally accepted as a matter of courtesy that a smoker should ask "do you mind if I smoke?" This became more and more prescriptive as health concerns increased over the use of tobacco. Now the "safer" option of vaping is becoming more common, and as of yet, there seem fewer "official" regulations on it (at least in the UK).
Should someone using an e-cigarette ask those nearby, and especially those they are with, "do you mind if I vape?" in a similar way as a smoker?
Asking if it's ok seems completely appropriate, particularly if you're in someone else's home or car.
Even though there may be a reduced health risk, most vape products have an odor that other people may not appreciate, and that smell may linger.
It may just be my perspective, but when making changes to a shared atmosphere it's appropriate to ask. Even with more innocuous things like adjusting the temperature, or turning on a radio, if you're with others and you're not sure, ask.
As a side note...
I've known a number of smokers who switched to vaping because it was less regulated. They could vape indoors in places where they couldn't smoke and so on.
Once upon a time smoking was common enough that people wouldn't think twice about lighting up in most places. As people became aware of the health issues, the etiquette adjusted and people were expected to ask or excuse themselves and go outside. My point is that the customs changed over time.
Vaping being a realitively new thing, the etiquette is still developing... But in a lot of places it seems to be being treated more and more like smoking.
Etiquette for new social phenomena will always be slow to develop.
I live in the United States, so your answer may vary, but years ago, I remember people vaping in shopping malls with no restraint, but now those same shopping malls have restrictions against smoking that explicitly includes vaping and e-cigarettes. And yet, I still see people vape in other indoor spaces with no repercussions despite these new restrictions in some areas. The idea that vaping = smoking, socially, hasn't caught on everywhere.
I feel that asking may be the most responsible thing to do in a public space. It allows the people around you to say no, which I think is the best indicator of what's polite or not amongst whatever group of people you're with or place you're in.
