Most financial advisors will recommend that you have an emergency fund. This could be for anything unexpected such as a job loss or major expenses like medical bills or home repairs. If you are saving money to purchase a new car, this would not count as part of an emergency fund. You are expecting to buy a new car. It is not being set aside for an "emergency".
I have seen advisors recommend anywhere from 3 months of living expenses to 9 months of living expenses. In this economy, perhaps it should be even more. But it is important to emphasize that each individual's situation is different.
If you are a 25-year old single male who makes $12 per hour and shares an apartment with two roommates, then a 9 month emergency fund is probably not necessary. Such an individual could probably find another job for something close to what he currently earns. And if his expenses are expected to stay low, then a smaller emergency fund would likely suffice.
This isn't to say that such an individual should stop saving. You need to save for retirement and future expenses. The 25-year old may want to purchase a house. Saving for a down payment would not be part of an emergency fund. But I see no reason that the person could not purchase a house (assuming it is affordable) if he had only a 6 month emergency fund as opposed to a 9 month emergency fund.
On the other hand, someone who earns $50,000 per year and supports a wife and children would probably want at least a 9 month emergency fund. It would not be a good idea to make other major purchases until that money is set aside.
I think there are also some gray areas in terms of what would be part of an emergency fund. Cash (technically digits) in a bank account is the obvious. It is liquid. Paying extra on your mortgage each month is about the opposite. It is not liquid at all, unless you are planning to sell your house or take out cash from a refinance. A 401k plan is another example of money that is not liquid, particularly if you are still employed with the same firm that holds your plan. You will not likely be able to access it unless you leave the company.
If you are in a situation where you need a 9 month emergency fund, here is my recommendation. Get 3 months of living expenses into the bank, either in a checking account, savings account, or money market fund. This is your most liquid money. For the other 6 months, I think it is acceptable to have investments that may not be liquid in one day, but is relatively easy to access in a short period of time. These could be investments in gold and silver (the physical metals). It could be stocks, mutual funds, and ETFs that are outside of a 401k plan. It could even be investments inside a Roth IRA, as you can at least withdraw your principal contributions without a penalty. But you should also account for any volatility that may take place in your investments.
In conclusion, I think it makes sense to have an emergency fund. This should be for unexpected expenses. It does not all have to be cash in the bank, but it should be relatively easy to access in case you need it. Each individual and family situation is different, so you should adjust according to your own needs.