There are three myths that bother me.
Predictor variables need to be normal.
The pooled/marginal distribution of $Y$ has to be normal.
Predictor variables should not be correlated, and if they are, some should be removed.
I believe that the first two come from misunderstanding the standard assumption about normality in an OLS linear regression, which assumes that the error terms, which are estimated by the residuals, are normal. It seems that people have misinterpreted this to mean that the pooled/marginal distribution of all $Y$ values has to be normal.
Indeed, as is mentioned in a comment, we still get a lot of what we like about OLS linear regression without having normal error terms, though we do not need a normal marginal distribution of $Y$ or normal features in order to have the OLS estimator coincide with maximum likelihood estimation.
For the myth about correlated predictors, I have two hypotheses.
People misinterpret the Gauss-Markov assumption about error term independence to mean that the predictors are independent.
People think they can eliminate features to get strong performance with fewer variables, decreasing the overfitting.
I understand the idea of dropping predictors in order to have less overfitting risk without sacrificing much of the information in your feature space, but that seems not to work out. My post here gets into why and links to further reading.