Reckon 3 months salary might be a stretch but 3 months expenditure might be more realistic.
I'm assuming when the suggestion was first coined, it was made for people for whom those 2 things are the same 
Life is generally not so short that your car might not need a major repair or your boiler break. Holidays are lovely but they're not nearly as relaxing as knowing you wont be torally up shit creek if there's a financial hiccup.
I agree with Barbarian on this, although I guess part of that is because I hate owing money, and would feel really stressed if I did (mortgage aside). I LOVE holidays, but in the lean years, that means a few days kipping on someone's floor in a different part of the country. I wouldn't be spending thousands seeking a holiday in the sun, if I didn't have the cash to cover an unexpected repair of boiler or car or replacement of fridge or washing machine.
I treat savings like every other bill. I wouldn't consider not paying the mortgage, the gas or the water. Nor will I skip on the savings. A set amount each month to buffer against life's inevitable hurdles.
I'm like this too. I've always had a standing order, on payday, in to a savings account. Yes, there have been periods in my life when I've had to take the money out again, but it has to be a 'conscious decision' to take the money out to be spent, rather than more casually using money that happens to be in my account. At that point I know I am choosing between what I want 'then' and what I am saving for - sometimes it had to be done, other times I've decided it isn't worth it.