Now 23-year-old student Tilly Cripwell is campaigning for Dublin Council to repair the statue and raise it to a less accessible level.
Unfortunately several tour operators have included the statue in their list of local attractions, encouraging more physical contact. Also an urban myth has emerged that touching the statue's breasts will bring good luck.
Dublin Council says it's considering the campaigner's requests and has asked for cost quotations for carrying out the work.
I've never actually seen the statue in situ but I can understand the objection to visitors casually groping her breasts as if that's okay ("It's only a statue" as some of them put it).
The Council could put up a "Do Not Touch" sign but how many people would take any notice?
Molly Malone isn't a real person of course. She was a legendary Dublin woman who sold shellfish in the city streets. She's the subject of a traditional folk song that's now the city's unofficial anthem.
Anyway, the next time I'm in Dublin I'll check out the statue - and see if anyone's fondling it.
PS: The lyrics are here: https://www.google.com/search?q=molly+malone+lyrics