Fan Death

So a natural question to ask is what other theories are widely believed despite lack of evidence.

A close analog is perhaps "do not swim 30 minutes after eating". (Apparently this concept dates back to at least 1908 [1], which would make it about the same age as the fan death). You can see the same historical tendencies as you see for fan death: it used to be very widely believed, but nowadays with the help of the internet people can fact check things easier, and it's starting to be debunked by Snopes and so on.

I forget who, but someone said that dietary advice is an analogue to fan death. That is, there is essentially no evidence that e.g. eating fat will make you fat, or that anti-oxidants are healthy, or whatever, but still each new nutrition-science fad is eagerly and credulously passed on.

[1] http://www.snopes.com/oldwives/hourwait.asp