Most experts will agree that one should have an emergency fund. What they all argue over, however, is just how big it should be. No matter what they recommend, I think the answer to this is very personal, and totally dependent on an individual's financial situation.
The closest thing to a consensus on this issue seems to be that you should have 3 to 6 months of living expenses in an emergency fund. The assumption in this case is that if you were to lose your job, you could survive without any income for long enough to find another comparable job, and in the job market for the last ten years or so, that could take 3 to 6 months.
If you work in a pizza parlor, then you can probably find another pizza parlor job in a week, so by this reasoning, you really only need to keep a week's salary in your emergency fund. But what about other types of emergencies, like an unexpected medical expense, the transmission going out on your car, or the water heater giving up the ghost? You can see that basing your emergency fund requirements on income replacement as a sole criteria might or might not work well.
I prefer to look at an emergency fund from the standpoint of having a cash cushion. Maybe it's my wargaming experience, but I also like to approach it with a strategy of having multiple layers of defense.
My first layer is a simple cash cushion in my checking account, that I don't write down in the checkbook. It's there basically for three reasons: 1) I might make a mistake in my arithmetic or forget to write something down, and end up with less than a zero balance in my account. If the cushion is there, no worries, no overdraft charges, and I keep on moving right along. 2) My wife might write a check or use the debit card for a purchase without looking at the balance in checking. If this happens, I'm covered, no worries. 3) I might run across a spectacularly good deal on something, and need immediate cash to buy it, I can use up to the amount in the cushion, and take advantage of my good luck.
My second layer is where I break from the experts. It's my Visa card. It has a high credit limit, and in most emergencies people have no problem accepting it for payment. When the fuel pump on my pickup truck died in the middle of the freeway, I used it to pay the tow truck driver and the repair shop. Since I never carry a balance from month to month, I pay no interest on the money I borrow with it. I hope that I never have to use it to cover living expenses for a long period of time, because that wouldn't be smart, but for most things, it's a quick solution to a problem, and I can use the grace period to access my next layer of defense. If you're the sort of person who cannot pay off their credit cards every month, or who carries a large balance, this is not a wise "emergency fund" choice.
My third layer is a "high yield" savings account online. If I need the money for something immediate I can have it transferred to my checking account overnight. It's highly liquid, and earns a typical rate of return for a savings account.
The fourth layer is some "naked" investments in stocks and mutual funds. These aren't tied up in my 401K or IRA, but are available for me to sell off as needed for cash. I can sell them well within the grace period on the credit card, though I might take a paper loss by doing so. If the loss is less than the interest rate hit for carrying the balance would be on the credit card, then it's a good decision.
As I said before, the emergency fund depends entirely on your personal situation, and a highly paid individual in a volatile profession with dependents might want to go with the 3 to 6 month salary option, but at the very least a person ought to have a bit of cash laying around somewhere safe, earning a spot of interest, for those odd emergencies we all experience, so as not to have to make a choice between eating or paying the heat bill.